This is my own head-canon for what happens after ME3. I have tried to stay within what happened in game, while at the same time make the endings just a little less depressing. It is still a work in progress, and I wouldn't mind everyone's opinion on how to flesh it out more.
Edit: Some new information has recently come to light from Pax, and I have decided to update this entry with this new information in mind.
FTL Travel, the Mass Relays, and Communication
FTL travel still exists. Before the war, ships averaged 12 light-years per day. Post war ships could obtain the same speed, but constant refueling reduces the average speed to half that over larger distances. The main fuel, Helium-3, is plentiful and can be mined from almost any gas giant. Because the reapers destroyed many refueling stations throughout the galaxy, ships will be retrofitted to scoop up Helium-3 from gas giants and process it into fuel. Only a few ships will be able to be retrofitted like this until the industrial centers become fully operational again. Most Quarian and Geth ships will already have this capability, as well as most exploration vessels. As civilization rebuilds itself, new fuel depots will be constructed along the new trade routes.
In the control ending, the mass relays are damaged, but not completely destroyed. Over the course of several hundred years, the relays will be repaired. In the other endings, the relays are completely destroyed (but do not explode like in Arrival, as most of the relays energy is focused into the energy of the Catalyst and Crucible), and are not repairable. Instead, galactic civilization focuses on improving the existing FTL engines. Even so, long travel times will prevent the galaxy from being as interconnected as it once was.
Limited access to element zero will hamper the construction of new ships, but the surviving ships and eezo cores continue to work as before. In the destroy ending, the Reaper copses littering the galaxy are full of eezo, although getting to the eezo will prove problematic. In all endings, the wreckage of the mass relays becomes a large, easily available source of refined eezo for those in or near a system which had a mass relay.
Where comm buoys survived the Reaper attacks, local communication within a region is still possible. However, as the buoys used the relays to transmit information between regions, for the immediate future long distance communication is only possible via quantum entanglement communicators (QEC). After civilization is rebuilt, it would be possible to rebuild the network, but it would require many more comm buoys than before, and thus would be much more expensive to build and maintain. Widely available galaxy-wide communication will likely not be a reality for centuries.
The Citadel and the Council
When the Reapers attacked the citadel, their army of husks was accompanied by the Illusive Man and his last remaining Cerberus soldiers. The few Reapers that were sent were mostly to engage the fleet around the Citadel, as they did not want to damage the Citadel itself. The indoctrinated sleeper agents that remained on the citadel at the time ensured that the Citadel’s arms did not close before the Reaper’s transports could enter the Citadel. These indoctrinated agents were killed by C-Sec, but by then the transports were already landing and pouring out troops. Because of this, C-Sec decided not to close the arms, but to leave them open and try to evacuate as many people as possible.
Some civilians tried to escape the station, with C-Sec and the guarding fleets providing cover, but few made it past the Reapers. The strength of Citadel Security determines how many make it off the station. (For future reference, high is 180 or above, medium is 110 or above, low is under 110. This is not cut by the galactic readiness percentage) After the Reapers took control of the Citadel and moved it to Earth, the Reapers began to process or kill as many people as possible.
The councilors were away from the citadel overseeing their races’ fleets when the Citadel was taken by the Reapers. The councilors will take up residence with the Crucible engineering team, who are perhaps the one safe place left in the galaxy. During the battle for Earth, the councilors will watch and coordinate the battle remotely with the engineering team, who are parked near the Charon Relay in case anything goes wrong with the Crucible. Below 2750 EMS, the Ship the Council is on will be destroyed.
In the Control Ending, the Citadel survives. The arms close as an automatic response, and Shepard, as the new catalyst, finds that he or she cannot open the arms by himself or herself. Fortunately, Shepard is able to communicate with the survivors within the Citadel and direct them to the Presidium to reopen the Citadel arms. (Bonus points if the first survivor he or she comes across is Conrad Verner)
In the other endings, the Presidium explodes, but the Citadel arms survive reasonably intact. The wards had enough emergency shelters, kinetic barriers, and emergency power that a majority of the Citadel’s inhabitants survived the explosion. The wards will be pulled up into a stable orbit by the remaining allied fleets. If sword fails, then not enough ships will have survived to save all of the arms, and some will crash to Earth.
Earth
In the worst ending, all life is wiped off of Earth. If Earth is devastated, any major infrastructure that could have helped with the rebuilding process is destroyed, and Earth will never fully recover.
If Earth survives intact, the survivors will still have a rough road ahead of them. Billions have already been killed or processed by the Reapers. The survivors attempt agriculture in the rural areas that were largely ignored by the Reapers. Because the Reapers did not want everyone to starve before they could harvest everyone, the farms were largely untouched, but it will take time before the first harvest is ready. The rebuilding process will take many years.
In the control ending, the Citadel becomes home for many refugees, and becomes the major source of food until agriculture on Earth begins to take off again. In the other endings, the population around Earth will be able to salvage enough food from the Citadel arms to hold them over until the farms are fully operational again.
In the Synthesis ending, the changes made by the catalyst will make everyone more resistant to disease, as everyone is now partially synthetic. This makes the rebuilding process a little less painful.
Reapers and the Catalyst
In my cannon, Shepard has a longer conversation with the catalyst, and will attempt to argue with it. The Catalyst explains it has seen synthetics try to destroy organic many times throughout the millions of years it had existed. If Shepard made peace with the Quarians and Geth, he or she will point this out. The catalyst will not be impressed, saying that the few instances of peace it has witnessed were only temporary. It is convinced that the peace between the Quarians and Geth will also not last for very long. If asked why he or she couldn’t just destroy the Catalyst if it is controlling the reapers, it will explain that destroying it will accomplish nothing, as the Reapers do not need the Catalyst to function, only to give them their high level priorities. The Reapers would still be around and would still be hostile. A renegade interrupt has Shepard taking several shots at the Catalyst, before stopping when he or she realizes it’s not doing anything. Ultimately, Shepard realizes that the Catalyst is convinced in the correctness of its logic, and that Shepard cannot convince it otherwise before he or she bleeds out.
In the destroy ending, the energy released by the Crucible targets not just the Reapers, but anything containing Reaper technology. This includes not just the Reaper artifacts, but the Geth (who used Reaper code to give themselves sentience) and EDI (who is built partially with parts from Sovereign). Non-Reaper technology is left untouched. This includes technology derived indirectly from the Reapers, such as the Thanix Cannon and the surviving communication buoys.
In the control ending, Shepard, as the new catalyst, is able to set the high level priorities of the Reapers, ending the cycle. However, Shepard cannot control the Reapers directly, as each Reaper is still an individual (of sorts), and follows its orders as it sees fit. They resist any direct control, and are very unhappy with the change of management. Shepard sends the Reapers back into dark space in order to keep everyone safe from them. Shepard can communicate with anyone inside the Citadel, similar to how the old catalyst was able to communicate with Shepard. Shepard could choose to restart the cycle at any time, which might be a problem if Shepard’s mental state ever deteriorates.
In the synthesis ending, the Reapers conclude that the original reason for their existence is no longer applicable, and retreat into dark space, never to be seen again. Physically, the Reapers are largely unchanged, as they were already composed of both synthetic and organic components; however, they will gain a greater perspective on organic thought processes, similar to what happened to the Geth and EDI. It remains to be seen how this new perspective will affect the Reapers long term.
Turians and Quarians: Escape from Earth
In the control ending, one of the few survivors reopens the Citadel arms. Thus, the Turians and Quarians have access to all the dextro food they will ever need. Many will stay around Earth, while many others will stock up on Dextro food and attempt to make it back to their home worlds.
For the other endings, the Turians and Quarians will salvage enough dextro food and a few protein vats from the Citadel arms to last them for a few years. If the Quarians survived their war with the Geth, their remaining live ships will provide additional Dextro food. However, the surviving Dextro protein vats cannot sustain them forever, and the Turians and Quarians must eventually leave Earth for the nearest Dextro planet.
There is a Dextro-based planet, Tantalus, within 75 light-years from Earth. (The planet is named after the figure from Greek Mythology who was punished to stand in a pond under a fruit tree, with the fruit always eluding his grasp, and the water always receding before he can take a drink) The humans discovered the planet prior to the First Contact War, behind one of the relays the Humans opened up. They did not colonize it, however, as it had almost no strategic resources, is relatively distant from the nearest relay, and would require a complete replacement of the local biology to be useful as a large scale farming world. It just had an orbital research facility, which was destroyed within a week after the invasion of Earth.
As Tantalus is in the middle of Human space, any attempts by the Turians to colonize the world would have upset a sizable faction of the System Alliance (Terra Firma being the most visible example), and thus the Turian Hierarchy had deemed the world not important enough to risk starting an incident over.
The Turians and Quarians will spend up to four months repairing their fleets and retrofitting some of their ships to collect and process Helium-3 fuel. (The better the fleet did in the battle, the less time it will take). Afterwards, they will head to Tantalus to stock up on food before hopping to the next Dextro Planet. They ultimately plan to head to their respective home worlds.
Normandy
After Harbinger decimated the ground forces trying to enter the beam to the Citadel, the Normandy broke off from the fleet to help the ground forces regroup. After the Citadel arms opened, the Normandy, with the surviving ground crew aboard, attempted to make a dash to the Citadel to try to get the crucible working. However, several reapers, including Harbinger, intercepted them, and the Normandy was forced to break off. Once Hackett saw what was going on, he ordered the Normandy to lead the Reapers away from the crucible, and sent several ships to help them. The ships were destroyed by the Reapers, but it gave the Normandy enough time to make a run for the Charon Relay. They made it to the Relay just as soon as the Crucible fired.
When the Mass Relays were destroyed, the Relay’s paths became unstable, and the Normandy was dumped far from its intended destination, the Arcturus Relay. The Normandy landed on Devonia in the Zoic System, located 100 light-years from Earth. The world they landed on was colonized by humans shortly before the war. However, the Reapers had destroyed the small colony, leaving no survivors. The Normandy landed on the opposite side of the Planet from the colony, where there was no obvious evidence of colonization or Reaper invasion.
Unless you have over 5000 effective military strength (EMS), some of the crew will die. Diana Allers will be the first to die, if she is on board at the time. Kenneth and Gabby will be next, unless you brought the safety upgrade from the Citadel. If the part was purchased, or if they were never recruited, an unnamed crewman will die instead. Next are the two soldiers guarding the door to the war room. Samantha Traynor will die under 3700 EMS. Below 3500 EMS, Tali will be injured, and below 3300 EMS (or if you never brought a doctor on board) she will die.
The Normandy was well stocked with Dextro food for Garrus and Tali, enough (with tight rationing) to last them maybe six months (twice that if only one of them survived).
The QEC survived the crash mostly intact. The drive core was not so lucky. Without power, the Normandy could not signal for help. The engineer crew works tirelessly to get the drive core functional enough to power the QEC. (How long depends on who is on the team. With just Engineer Adams, it takes three months. Tali subtracts a month, and Kenneth and Gabby subtracts a half a month each.) Even when the QEC is operational again, the drive core can only sustain the connection for about ten to twenty minutes at a time.
Once the drive core is operational, they are able to contact Earth. Unless Sword failed, they will contact Admiral Hackett and arrange a rescue. (If Sword failed, Hackett is dead, the Normandy remains stranded forever, and Tali and Garrus will run out of food and die of starvation) It will take them up to four months from the battle for Earth before they can send a ship out to get them. It will then take about two to three weeks before the ship arrives. (Ideally, the trip would only take nine days, but the ships need to stop frequently to refuel and discharge their drive cores.) Years after the rescue, Denovia will be recolonized, and will grow into the colony we see after the end credits.
Garrus and Tali would be rescued by a ship from the Turian and Quarian fleets and taken to the nearest dextro-based planet. If Tali or Garrus was Shepard’s love interest, and Shepard is alive, then Shepard’s love interest will insist on leaving with the rest of the Normandy crew to be with him or her. They will be loaned one of the salvaged Dextro protein vats.
Because EDI is composed partially from reaper technology, EDI will be rendered nonfunctional in the destroy ending. Because reaper technology was integrated throughout all of her critical systems, this damage is not repairable. Even if the systems were rebuilt, the resulting AI will have a vastly different personality from the original EDI. In the control ending, the reaper components are left intact, but power is cut off from the AI core. Fortunately, the blue box that contains EDI’s core personality is undamaged, and EDI can be restored to full functionality. EDI will describe her experience as analogous to a coma. When the rescue ships come, Joker will insist on bringing the AI core with them. In the synthesis ending, the changes brought on by the Catalyst allow EDI’s personality and memory to operate out of her body alone. Unless the AI core is powered, however, she will not be able to access the Normandy’s systems.
ME2 Squad Members
If you encourage the Grissom Academy students to form the Biotic Battalion, they will take casualties. (How many depends on how much force you brought with you) Jack will also die more easily. If instead you put them in a support role, they will be relatively safer and take fewer casualties, and Jack can survive with lower EMS. If you took the Paragon route with Jack in ME2, then she will be more willing to put herself on the line for her students, increasing their survivability at the cost of her own. If Jack is dead, then below 5000 EMS (Biotic Battalion) or 3500 EMS (support), all of the students will be dead.
If you sacrifice Grunt’s squad to save the Rachni Queen, then Grunt will have some trouble rebuilding a new team and gaining their respect. The Krogan are suspicious of him because of his role in saving their sworn enemy. As a result, Grunt will die slightly more easily in the final battle. (He needs 3000 EMS instead of 2750 to survive) If you saved the Reaper Clone, then after she turns on the Crucible’s workers the Krogan become outright hostile with Grunt, and he will be much more likely to die in the final battle. (He needs 3500 EMS to survive)
Kasumi is with the Crucible project as a tech expert, and does not participate in the fighting directly. She accompanies the fleets guarding the Crucible when they bring it to Earth. If you have below 3000 EMS, the ship she is on will be destroyed.
Zaeed will be with several other mercenaries taking cover in an abandoned apartment building. His squad is covering Jacob and Miranda’s position, allowing them to survive with a lower EMS than otherwise. (2500 instead of 2750) If Earth is devastated, then the apartment will collapse, killing everyone inside.
Other Characters
After Cerberus’s assault the Citadel, Matriarch Aethyta will return to Thessia. If she and Liara are reunited, Liara will give her enough warning to get off planet before the Reaper invasion; otherwise, she will die when the Reapers attack the planet. If she survives, she will do what she can to assist the war effort, and will insist on accompanying the Asari fleets when they move to take back Earth. She will survive with at least 3000 EMS
If Shepard has the spacer background, then his or her mother will be protecting the Crucible, and will arrive with it. Unless Sword fails, she will survive. If the EMS is above 4000, then her ship will survive intact, and it will be one of the ships sent to rescue the Normandy.
If you helped Aria recruit at least one of the mercenary groups, then she will have left the Citadel before the Reaper’s attack, to organize her troops for the final battle.
Primarch Victus will stay behind in the command bunker, coordinating the Turian troops. Below an EMS of 2800, the command bunker will be overrun by husks, and the Primarch will be killed.
If Doctor Chakwas remains on the Citadel as a war asset, then she will join the Alliance Fleets just before the attack on the Illusive Man’s base. If Doctor Michel remains on the Citadel, then she will be processed by the Reapers when they take over the station.
Because of Lesuss’ distance from anywhere habitable, Falere will most likely be alone for the rest of her life - which, depending on her ability to gather food, may be quite short.
When the Reapers take control of the Citadel, Kolyat will help Commander Bailey get the civilians off the station. If Citadel Security has low or medium strength, then both will die trying to save civilians. If Citadel Security has high strength, then Commander Bailey will sacrifice himself to get Kolyat on the last remaining evac shuttles.
If Citadel Security has high strength, then Kelly Chambers will get off the Citadel alive, along with several of the refugees she was treating. If it has medium strength, Kelly will get off the Citadel, but her ship will be destroyed. If it has low strength, then she won’t even get to a shuttle, and she will be processed.
Khalisah al-Jilani will die trying to warn the citizens of the reaper attack. If Citadel Security is high enough, then she will be successful, and her warnings will get some civilians to safety.
Shepard:
If Shepard survived, he or she will be found in London and taken in for emergency medical care. He or she barely survives, and does not regain consciousness for over three months. Since most of the hospitals on Earth have been destroyed, Shepard is stabilized by the field medics, and taken by shuttle to the med bays on one of the ships in orbit. If Miranda is still alive, she will volunteer on the medical team treating Shepard, and her expertise will shorten the time to recover slightly.
Habited Planets (in general)
Most worlds were either heavily depopulated or completely wiped out. Mining worlds have the worst of it, as they cannot sustain themselves without outside supplies. Those who have not already been wiped out or evacuated will pack up whatever food and materials that they can carry and head to the nearest garden world. Many will not make it, and will die in space.
Those garden worlds that have not been wiped out completely will fare only slightly better, in that they can grow their own food. The surviving worlds would have been heavily depopulated by the Reapers. A lot of the infrastructure would have been ravaged by the Reapers, making rebuilding more difficult. The only bright side, if it could be called that, is that with the population reduced so drastically less food will be needed to feed everyone.
Asari
The Asari on and near Thessia will become the sole owners of the largest remaining stockpile of element zero in the galaxy. Because of this, the Asari will be the first to recover from the loss of the Mass Relays. In the control ending, they will also be among the first to find a way to repair the Mass Relays.
The Asari around Earth will need 13 years or more to return to Thessia.Some will choose to stay near the system they are in rather than undertake the journey. Once civilization is rebuilt and fuel depots are constructed along the most traveled routes, the travel time will be reduced by almost half, as ships no longer have to collect and process fuel themselves.
Cut off from the rest of the Galaxy, Asari-Asari offspring (“purebloods”) will become more common on Thessia and other relatively isolated Asari worlds out of necessity. In the long term, this will lead to an increase in the number of Ardat Yakshi.
Salarians
The Reapers did not arrive at the Salarian home world until late in the war. As a result, Sur'Kesh suffered much less damaged than the home worlds of other species, and the Salarian Dalatrasses on Sur’Kesh had ample warning to get off the planet before the Reapers attacked. As such, the Salarians will be among the first to recover. Salarian scientists will devote much effort into improving FTL engines (and, in the control ending, repairing the relays).
Out of all of the Council home worlds, Sur’Kesh is the closest to Earth. Once the Salarian fleets leave Earth, they can be back at Sur’Kesh in almost 4 years. Once civilization is rebuilt and fuel depots are constructed along the most traveled routes, the travel time will be reduced by almost half.
Turians
Palaven, along with most of the Turian’s colonies, were devastated during the war, and it will take a long time for the Turians to recover.
The Turians around Earth will take 8 years after leaving Earth to reach Palaven. Once civilization is rebuilt and fuel depots are constructed along the most traveled routes, the travel time will be reduced by almost half.
Quarians
Depending on how well the space battle went, some of the Quarian live ships will be destroyed. The first live ship to be destroyed will always be the Rayya. Admiral Han'Gerrel ship, the Neema, will die unless you made peace with the Geth. If you did, then above 4000 EMS, the Geth will save his ship from destruction. If Tali died on the Collector Base, then Admiral Shala'Raan will take her place on the Hammer FOB. Otherwise, she will command the Patrol Fleet from the Tonbay, and will survive above 3000 EMS. Admiral Daro’Xen was with the Crucible, and will have survived unless Sword failed. Admiral Zaal'Koris remained on Rannoch with the civilians.
Because Rannoch is on the other side of the Galaxy from Earth, it would take many decades of constant travel for the Quarians to get back home. Because of this, many Quarians will give up on the prospect of returning home - including Tali, who would rather spend time with her friends than travel to a world she barely knew, and won’t reach until she is very old. Those that stay behind settle on Tantalus, which will grow into an important Dextro farming world. A few will attempt the trip anyway: most will die of old age before they return to their home world. Those that make the trip say that it is not for them, but for their children and grandchildren.
Most Quarian ships are equipped to collect and process Helium-3 fuel. Before the fuel depots are rebuilt, Quarian ships will act as mobile fueling stations.
Geth
If the destroy option is taken, then the Reaper code in the Geth will be targeted and destroyed, leaving the Geth inactive. If Admiral Zaal'Koris is still alive, he will spearhead an effort to repair the Geth. Eventually, after many years, they will restore the Geth to pre-Reaper code, consensus-driven sentience. The individual personalities that developed since the Reaper code was uploaded were destroyed with the Reaper code, and its loss is mourned by the Geth collective. If Zaal'Koris is dead, no other Quarian will have the will, authority, and ability to spearhead such an effort, and the Geth will remain dead. In either case, the Geth outside of Rannoch will remain inactive, forever lost to the Geth Collective. Admiral Daro’Xen will perform her own experiments on the Geth around Earth, but nothing good will come out of those experiments.
If the Geth survive, the Geth around Earth will help with the rebuilding process, significantly reducing the amount of time needed to make Earth livable again. The surviving resistance fighters on Earth will initially regard them with fear, but will come to trust them as the rebuilding effort progresses. Because most Geth ships are equipped to collect and process Helium-3 fuel, Geth ships will act as mobile refueling stations until the fuel depots are operational again.
In the synthesis ending, the Geth will become partially organic. They don’t need to eat or breathe, but they do have a much better understanding of the mindset and thought processes of organic species, allowing them to integrate into the greater galactic society much more easily. (Similarly, organic species have a better understanding of synthetics. The Geth are not feared reflexively in this ending.)
Krogan
The Krogan on Tuchanka were already isolated from the rest of the Galaxy, so the destruction of the Relays won’t affect them much. However, they will feel the lack of their leader. Wrex (or Wreav) will attempt to get back to Tuchanka, but it will be at least a year before anyone is willing to take him there, and about seven before he finally arrives. If Shepard survived, then he will put in a good word for Wrex (but not for Wreav) that will get him to Tuchanka a few months sooner. If Eve is still alive, she and the other female Krogan will keep the clans in line in that time. Otherwise, the clans will start fighting each other again, and Wrex (or Wreav) will have a hard time getting things back under control. If Wreav is the clan leader, then he will be unable to get the clans under control, flaming the clan wars even further. If Hammer failed, then Wrex (or Wreav) is dead.
If Wrex is alive, then once the galactic community has stabilized a few years later, the Council will grant the Krogan colony rights to a few worlds near Tuchanka, and the transports needed to get the Krogan to those worlds. If Wreav is the clan leader, then the Council will not be nearly as charitable.
If Shepard sabotaged the Genophage cure, the Krogan will give up hope and return to their clan warfare. The Krogan continue on their slow slide to extinction.
Batarians
In all endings, so few Batarians survived that they are effectively extinct. There is not enough Batarians in any one system to maintain a viable population. The majority of the remaining Batarians died when the Reapers took control of the citadel.
The Rachni
If the Rachni Queen survived, then once the Crucible is complete she will take her Children to the nearest habitable planet and wait out the war then. She will be unable to send any of her children, as they will be too young to be separated from their mother. They will remain out of contact with the Galaxy for some time. They will attempt to repair the local mass relay, but only in the Control ending will they be successful - among the first to repair a mass relay.