I like the ones that start out jaded or shitty in the beginning, but grow to be better people as the story progresses. I've noticed that some of the best books I've ever read involve protagonists like that. They start out like complete shit-heads...and then by the end of the book they're like, "I LOVE PEOPLE, OMG!"
Songmaster by Orson Scott Card is one; I'd read it despite all the hype he gets over the Internet for being a homophobe. The guy probably can't figure out whose side he's on, but damn can he write. (The book's also a weird mixture of fantasy, science fiction, and modernism. It made me think of Lord of the Rings in Space.)
The World Ends With You is another example, only it's a video game. I suppose minus the game play, it can be a visual novel. And it pretty much is. It has all those themes in it that get me right in the heart muscle. Learning and growing as a character. Experiencing a side of life no one else gets to and finding out what it means to be alive.
Well the protagonist Ansset starts out as this virtually emotionless being, despite being human, which causes him to act like an ass to his friends and elders. At the time, he can sing like nobody's business. Over time, however, he loses his singing abilities, but learns how to be emotional. So he may not be able to sing like Josh Groban, but he gets the message across anyway, because he can feel. It also helps that he's kind of psychic. He knows what people are feeling/thinking ahead of time before he sings. So he can put those thoughts and emotions into his songs before he sings. In doing so, this makes him extremely famous. It's kinda cheating, I think, but hey! It's the hardships he goes through down the line that really make you involved with him and his story. I guess that's why the ending (which I won't spoil) had me crying like a bitch for two days.