There are plenty of iconic characters with many great games to their name: DK, Mario, and Link to name a few, but none of them really have anything more than a surface personality in the games. From a character standpoint, I have to say my favorite is Old Snake from MGS4.
He doesn't have a ton of memorable quotes, but I really empathized with him a lot. Even so, just the little things he does in the game-groaning while executing a difficult maneuver, stretching out his sore back-really fill out his character.
The fatalistic hero aspect of his character really resonated with me, especially since it was such a change from the common archetypes of the upcoming kid, the stoic, the dark hero with the mysterious/messed up past, etc(and, of course, who wants to be an old man with no sword? Not cool guys.) He was old and in a lot of ways didn't want to be there. No one really believed in him anymore. For the most part, he was a used part in a machine. But at the same time, there was no other choice than to do what he did. It was the only thing left to give him any meaning in his life. Old Snake really pulled me into the story, along with the possibility that even if he won, it would really be everyone but him who got to enjoy the happy ending he spent his life fighting for. And there were some intense sequences in that game. Amazing.