Which gamer has most influenced how you play?
Can I just say first, for a moment, how much better these questions have been than years past?
My answer is my friend Scott, who tended to immerse himself in a character without being a scenery-chewing hack, was totally comfortable letting other people have their moment, and cared about other players (he's the guy with the bronze d20 in an earlier answer).
He's also a great GM, although he's such an Old School relic that he calls himself a "judge." I like that terminology because it implies that the role is one of objective reporting rather than controlling the game as a "master." His sessions were always detailed with an emphasis not on setting up a big combat, but rather leading the group into making critical decisions about the outcome. Much like his way of playing, Scott's methodology and philosophy could be described as someone who is a generous host, or guest, who sees their role at the party as ensuring that everyone else has a really good time. And that's cool.