Absolutely. This may betray the differences in the way we gamers game, but I always make idealized versions of myself that match the game's aesthetic. Idealized isn't quite the right word. I ask myself, "what would I look like if I were a part of this world?" So even if it's an elf, it's still me, just with pointy ears and a sick six pack. That's one damn sexy elf. Sometimes I transverse sex boundaries with female versions of myself, particularly in MMOs and online games, but that's dangerous for the obvious reason: invariably, I will fall in love with myself. To be entirely fair, I think that sometimes happens with my male characters, too.
I insert my character into the worlds in order to explore them to the fullest extent. So I can get closer to their experience. Interactivity is the name of the game here, right? And besides I'm not normally a great fan of consumer entertainment culture, the protagonists often inspire hatred or disinterest more than affection, so it's best if I just handle that side of things myself.
And once Digital Me is in his own little world, he's free to do all of the fun things for which I'd be torn down in the streets in the real world. And it's bliss.