I started reading George RR Martin’s A Song of Ice and Fire series in middle school–I recall reading book 2 while sitting in a tree at one point– and have kept up with it for a long decade and a half at this point. I was and remain a dedicated northerner, somewhere between a Stark and an Umber, I sympathized with Jon Snow, liked Arya Stark, and connected the most with Ned Stark. I still like these characters and have developed affection for other characters in subsequent books, but of the characters who have survived from the first book to the most recent, the one I find most interesting is one who I hated (as GRRM surely intended) at the outset: Jaime Lannister.
The reason I find him so interesting is that, when he is first introduced, he is arrogant, insolent, and really all you know is that he is a good fighter and he is sleeping with his sister. The impression you are left with is that Jaime is a bit of a dunce and a jock. Tyrion is the brains in the family, and it is certainly true that, compared with Tyrion, Jaime is a dunce. But, then, most of the characters in the series are. Once you get inside Jaime’s head, though, the story starts to change.
I do not believe that Jaime is actually stupid at any point in the series, but his intelligence is masked because he lacks ambition or the need to do anything differently. When you meet him in the first book, he has exactly two goals in life: to be the greatest swordsman in the world and to screw his sister. He is the former, through innate ability and training, and with his sister being queen he gets the latter. His life is straightforward and simple and he doesn’t need to be or do anything else. When he loses his hand, things begin change because he is forced to adapt. He still isn’t a genius, but he isn’t a dunce, getting by on a combination of skill and reputation. At the same time he has particular recollections of the generation of heroic warriors who accepted him into their brotherhood when he was a teenager and who those people were.
Other characters are nicer and there are others who I connect with more or who I would characterize as my favorite in a given book, but there is no character around for more than half of the books who I find as interesting. That is why Jaime Lannister is my favorite character in the series.