Jaime would be the classic hero if it wasn't for his relationship with Cercei. Think about it. He's a dashing warrior that helped win the throne and bring peace to the land. Then a the man who took the throne was a drunk who cheated on Jaime's sister and bankrupted the country. If the incident with Bran hadn't happened, he would be a hero in the story.
I also like how his dynamic changes when he learns about honor, justice and suffers his "injury" and has to reinvent himself. He's a very interesting character. Tyrion is still my favorite, though.