General background:
The year is unspecified. It's at least a hundred years in the future. Earth was united under the government of the Federation, which extended to most of the space colonies in the Earth Sphere, and colonization extended to Mars and Jupiter as well.
All sorts of mecha have become prominent and ubiquitous. Gundams abound.
The watershed event is Second Impact, 15 years before game start. Some disasters and threats occurred or began before it, some after it, but many coincided with it.
Festum had been attacking Japan for years before Impact.
The Getter team had been fighting the Dinosaur Empire.
In the run up to Second Impact, war breaks out between the Federation and the colonies threatened by the steps it's taking to prepare. This war causes considerable destruction.
Second Impact itself devastates the world, especially Asia. America is also hard hit, and much of the Antarctic ice sheet melts. Earth's orbit becomes choked with debris and meteorite impacts become a hazard.
Post-Impact, an Irgelion fleet attempts to invade the outer colonies but Earth itself doesn't pay much attention.
Tthe One Year War causes devastation.
Neuroi appear and start trying to eat places.
State of affairs:
Europe and Africa are the least hard-hit by the disasters. Much of Europe is under the control of Britannia, which also has a corporate empire including much of what's left of Japan. The rest of Europe and most of Africa is Federation territory. The Japanese Disaspora has created the nation of Fuso around the Pacific Rim, especially on the west coast of North America.
North America contains mobile cities roaming the wasteland.
Much of East and Southeast Asia was united under Gucun post-Impact, and since that nation's collapse is in chaos.
Northeast Asia is the land of the Domeopolii and the Siberian Railway.
Australia and South America are largely blank slates.
Global communication and commerce are in shambles. Standards of living are reasonably high in Britannia and the Federation but outside their territories networks are local and trade relies on barter or intrinsically valuable goods.
Travel to and from space is difficult due to the debris field and requires either motherships or exceptional mechs.
Many space colonies are self-sufficient enough to feel less hardship from Impact, but are in a political tight spot caught between the Titans and Axis.
Dropped canons:
_ Revolution Abraxas
Bliss Stage
Part of San Francisco was sealed away in The Bliss between 8AI and 15AI (game start).
Code Geass
Britannia occupies much of what's left of the Japanese archipelago to mine sakuradite.
Del Segno al Coda
Digimon Xros Wars
Galaxy Angel
The Transbaal Empire exists at the edge of the system.
Guitar Robo
Martian Successor Nadesico
Jovian Lizards are at war with humanity. Nergal Heavy Industries exists and has provided support to the Chalice in the past.
Megaman
Shin Mazinger Shougeki! Z-Hen
Strange Loop
Super Robot Wars Alpha Series
Super Robot Wars J
Super Robot Wars OGs
Tengen Toppa Gurren Lagann
Kamina and Simon came from Gaia - the same world as Escaflowne and Vandread.
Tesseki Garou
The Inanity Project
The Silver Trigger
Transformers Animated
Cybertron exists and is known to the residents of Cosmic Ark.
Visions of Escaflowne
There exists a parallel world called Gaia from which Earth can be seen in the sky. Somehow, some parts of that world were transported to or merged with our own (in part of North America).
World Egg
Zoids Chaotic Century
Zwei Hildebrandsleid
Hitler escaped the end of WWII by traveling in to the future. The world is full of incredibly strange things.
Pending canons:
In the Footsteps of Father
Kaizoku Sentai Gokaiger
Rinne no Lagrange
Humans possessed an advanced civiliization thousands of year ago which migrated to the stars and still exists today.
Being Lan is suffering.
Active original canons:
A Fistful of Science!
Five "Houses" exist as branches of a secret scientific society with holdings in various parts of the world.
Aethereal Wake
And Though I Walk
Arduus Umbris
Giant monsters called Colossi roam parts of the Earth.
Astral Frontier
Irgelions, an advanced race of astonishingly human-like aliens, exist and attempted to invade Earth in 4AI. They launched a fleet that was defeated in the outer colonies and its population absorbed there.
Das Leiden
Frame Rider Technica
Shapeshifting aliens called Percolati are infiltrating Earth.
Gundam Ragnarok
Ironlock
Much of Southeast Asia used to be a nation called Gucun for a while after Second Impact. It isn't anymore.
Kamen Rider Vita
Lost in the Cold
Project PreDesu
A magical alien McGuffin called the Rainbow Jewel powers a paramilitary group of magical girl mecha with several generations of teams fighting several successive waves of enemies, using the world's premiere amusement park, Fairy Park, as their base and front.
Record of the Atlantis War
Holy crap, Atlantis is real too.
Roar That Shaped Fate
Scales of Balance
A cult called the Disciples of Baphomet is trying to wipe out humanity or force us to revert to harmony with nature. Chibi robots that turn into giant OP super robots are apparently their natural enemies.
Still Not Safe
Shifting Entity attacks in Europe and North Africa destroy one city when they first appear (killing millions) and one more before they're stopped (killing many, but fewer thanks to one Shifter's sacrifice).
Wayward Signet Origins
Active established canons:
Ace Combat
The continent of Usea exists somewhere and has powerful ground-to-space weapon installations to defend against space debris.
Armored Core For Answer
The League of Ruling Corporations is powerful and mercenary.
Battletech
The Clans exist in the future or a parallel dimension.
Cosmic Break
Cosmic Ark exists and seems like a pretty awesome place.
Demonbane
Interdimensional magic is real. The city of Arkham has somehow been transported to East Asia.
Fafner in the Azure
Even before Second Impact, Festum had eaten much of the landmass of Japan and sterilized its population.
Getter Robo
Musashi Tomoe blew up New York to defeat the Dinosaur Empire.
Then, Invaders.
The destruction of New York and the appearance of Shin Dragon both contributed to the state of the world.
The Super Robot Army is a force to be reckoned with.
Starvengers lol.
Idolm@ster Xenoglossia
Fuso uses alien-black-box mecha called iDols to defend the surface against falling debris from Second Impact.
Infinite Stratos
The nations and colonies of the Earth Sphere send representatives to IS Academy.
Kamen Rider Decade
Kamen Rider Fourze
Kamen Rider Ryuuki
Kamen Rider W
Magical Girl Lyrical Nanoha
The TSAB patrols other worlds/dimensions.
Megas XLR
Metal Wolf Chaos
Neo America is currently subject to a coup.
Metroid
Samus comes from a future time, alternate dimension, or coincidental galaxy.
Misadventures of Tron Bonne
Mobile Suit Gundam
The One Year War in 9AI killed hundreds of millions. On Earth, fighting was mostly confined to Federation territory.
Mobile Suit Gundam 0080
Mobile Suit Gundam 0083
Mobile Suit Zeta Gundam
Mobile Suit Double Zeta Gundam
Mobile Suit Crossbone Gundam
The Jupiter Empire exists. The Crossbone Vanguard have some history, too.
G-Savior
Mobile Suit Gundam 00
Celestial Being have been intervening in conflicts using advanced tech since at least the One Year War.
Mobile Suit Gundam SEED Astray
Mobile Fighter G Gundam
The Neo colonies participate in the Gundam Fight.
Mortal Engines
Much of North America is roamed by mobile cities.
My Otome
Windbloom exists as a nation on the east coast of North America. Otome are a factor in world politics.
Neon Genesis Evangelion
NERV exists and has been significant in defending what's left of Japan. Angel attacks are among the "giant monster" threats along with Festum, Invaders and Neuroi.
Overman King Gainer
The Siberian Railway monopolizes trade and travel among the Domeopoli of northeast Asia.
Power Rangers RPM
Corinth, a city-state in Sri Lanka, was sealed off from the rest of the world - which it thought destroyed - for years, until recently.
Robotech
Strike Witches
Britannia organizes young magic-users from around the world to fight Neuroi attacks beginning in 14AI.
Super Robot Wars D
Super Robot Wars L
Vandread
In a (possibly alternate) future, a human colony effort becomes divided into two worlds segregated by gender. Further in that future, descendants of humans become parasitic Harvesters. (This is the same universe as the Gaia of Escaflowne and TTGL.)
Zoids New Century