I made a post on this below, but... just keep in mind that when you root for Jaime, you're rooting for the guy who caused literally every bad thing that's ever happened on this show....
It wasn't just Jaime pushing Bran out the window; it was Jaime fucking his sister and fathering children with her. Jaime tried to kill Bran to keep his sister-fucking a secret. Bran's attempted assassination was presumably done for the same reasons, and it was that which caused Catelyn to kidnap Tyrion (the assassin, who was assassinating to cover up Jaime's sister-fucking, used Tyrion's dagger). Littlefinger did his manipulations to keep Joffrey on the throne, which would never have been needed if Joffrey was actually Robert's real son (i.e., if Jaime had never fucked his sister).
Cersei killed Robert to get Joffrey on the throne before people figured out that Joffrey wasn't Robert's son, which, again, wouldn't have been necessary if Jaime had never fucked his sister, and if Joffrey was actually Robert's son.
Jaime isn't responsible for Khal Drogo dying, but if Jaime hadn't killed the Mad King (no matter how noble his reasons), Dany wouldn't have left Westeros in the first place.