This is something that always puzzled me : why is everyone , literally everyone hates Jaime for what he did to king Aerys II? I have just re-read some Brienne's chapters where she meets some ordinary people and they say things like: "Jaime Lannister is an evil Kingslayer". Doesn't this seem to be a little unfair? I mean, killing the Mad King that was about to burn up the city was a good thing to do?
However, the cause-effect chain is quite interesting, and I think the answer for the universtal hate of Jaime is actually in the way the events unfolded.
Two paragraphs below are taken from Wiki of Ice and Fire and contain the short synopsis of the events:
"Lord Tywin Lannister, who had remained neutral until the Battle of the Trident, marched to the gates of King's Landing with a force of 12, 000 men, claiming loyalty to Aerys II and asking to be let in. Aerys favored the advice of Grand Maester Pycelle over that of his spymaster Varys and opened the gates of the city. The Lannister forces then began to sack the city in Robert's name. Aerys ordered his most recent Hand, the pyromancer Rossart, to ignite the wildfire caches throughout the city, saying, "Let him [Robert] be king over charred bones and cooked meat. Let him be the king of ashes."
Aerys then ordered Jaime Lannister, one of his Kingsguard and Tywin's own son, to kill his father. Instead, Jaime slew Lord Rossart and then murdered Aerys himself on the Iron Throne. Tywin sent his knights Ser Gregor Clegane and Ser Amory Lorch to deal with the rest of the royal family, securing the throne for Robert and proving that House Lannister had forsaken the Targaryens forever. Gregor killed the baby crown prince Aegon Targaryen while his mother watched, and then proceeded to rape and murder Princess Elia herself. Amory dragged princess Rhaenys from under her father's bed and killed her. When Eddard Stark arrived shortly thereafter, he found Jaime seated on the Iron Throne and Aerys's corpse slumped below it. Tywin Lannister presented the bodies of Elia, Aegon and Rhaenys as tokens of his fealty, laid out beneath the Iron Throne. The resulting argument led to Eddard Stark riding out alone to finish the war in the south. "
From this, Jaime's killing of the Mad King can be viewed as a part of the bigger betrayal by Lord Tywin. This resulted in sack of King's Landing: babies murdered, women raped, etc. So I think it is easy to understand that the onlookers take the event as a whole, and instead of dividing it into "who did what" have a negative perception of the event. From what we know of Gregor Clegane and Amory Lorch, the whole city must have suffered rapes and killings. Even more, King Aerys order to burn the city was issued after the sacking of the city already started, so in the cause-event chain, the sacking of the city is the beginning of everything. But this I think is less relevant - not many people seem to know that Aerys intended to burn the city (but unfortunately this is the main argument for Jaime's actions).
As to Jaime, I think he did the right thing by killing Aerys and his pyromancer. Some can argue that there was a chance for Jaime to imprison the Mad King, but if this would have happened, the King Arys would have been killed by Ser Gregor only a little later. There was no way for the King to be out of this alive.
But is Jaime clear of any blame for the Sack of King's Landing? I don't think so. He was, after all, an accessory, as Jaime's murder of the Mad King was an integral part of the events. And in the mind of ordinary people he was the son of Lord Tywin , the man behind the Sack.
What I am trying to say is that whatever I might think of killing the mad King Aerys II (kill him, I say :D) , the events are much more complex than that and the King's death is viewed in people's mind as a part of the whole "rape and kill" event that took place in King's Landing. Which, obviously, was horrific..
In particular, it is clear why Ned Stark was so angry with Jaime: he sees Jaime on the Iron Throne, the King dead. It is not clear if the bodies of the family were already laid out in the front of the Iron Throne, but even if they were not, they would be shortly later... Ned , obviously, was not pleased with this (in fact, the killing of the Royal family is something that will haunt him for years) and the argument between him and Lannisters resulted from here.
It is not clear if painting everyone with the same brush is the right thing to do, but it is a natural thing that happens so easily. Plus, purely objectively, Jaime was an accomplice of Lord Tywin (he was there, he killed the King, he did nothing to stop other atrocities), and by proxy, an accomplice of Ser Gregor and Amory Lorch.
Hmm, everything seems so complex! In short, I think poor Jaime is painted with the same brush as Lord Tywin here, and it is interesting that at the end, he is maimed and tortured by his father's people, the same people that did the Sack of King's Landing. The circle is completed. Jaime has paid the price - his right hand, the same hand that killed the Mad King