Jaime Lannister was born handsome, rich, and privileged. Unfortunately, he was also born to a father who had no interest in his children beyond how they could profit him, so he had ample time to misbehave, which in his case meant falling in love with his twin sister Cersei.
They kept up their affair through adolescence, when Jaime became a member of Aerys Targaryen’s Kingsguard. They were still at it when Jaime killed Aerys Targaryen to stop him from exploding King’s Landing, and they were doing it right up until Robb Stark captured Jaime during the War of the Five Kings.
For better or worse, Catelyn Stark decided that Jaime was better off being returned to King’s Landing than a prisoner in Robb’s camp, and set him free with Brienne of Tarth as a chaperone. The trip went pretty smoothly, except that Jaime lost his hand, fought a bear, and developed confusing feelings of respect and affection for Brienne, but hey — he got back to town.
After his adventures away, it was difficult for Jaime to pick up with Cersei where they’d left off, but their relationship experienced a revival after Jaime tried and failed to bring their daughter Myrcella back from Dorne. (Oh, yeah — They had three incestuous children together. Don’t tell anybody.) He was devoted to her for a while, but when he returned from a mission away to find that she had blown up a small part of King’s Landing in his absence, he seemed none too pleased.
Jaime Lannister remains by Cersei’s side. But he’s in a weird place. After all, his sister-lover has done exactly what he killed the Mad King to prevent. Might this spell doom for this incredibly dysfunctional relationship that never should have started in the first place? God, I hope so.
There’s also the question of how Jaime will react when Daenerys and her advisors — specifically Jaime’s brother Tyrion — arrive in Westeros. Jaime has had it out for Tyrion ever since Tyrion killed their father Tywin, but striking an alliance with him and Dany may be preferable to serving the woman who blew up several hundred innocent civilians in a power grab.
So in a nutshell, Jaime has family issues.