Since I can't really think of a specific character that I really, really identified with in most of the games I've played, I'd have to say Tommy from Prey, because he acts exactly, and I mean EXACTLY how I would in the situation he's placed in. He has a bad case of "reluctant hero," his exclamations during the game were EXACTLY THE SAME AS MINE (no joke, straight down to the "I hate these fuckin' robots" after seeing the same enemy five times in a row).
He's hilarious and it gives the game happier overtones than it should have.