Robin's Laws has already been mentioned, but not detailed. It's one of the better ones to go by as it is descriptive and not pejorative.

The Storyteller - pretty self explanatory, the person who's interested in having a story be told, and being a part of it.

The Method Actor - the counterpart to the story teller, but this player likes to get into character for its own sake, rather than the outcome of the story.

The Specialist - the person who always plays a Ninja or a Halfling or an outcast evil character who has switched to the side of good.

The Butt-Kicker - self explanatory, happy if butt gets kicked. Not so happy if there are no fights.

Tactician - likes overcoming overwhelming odds or dealing most efficiently with resources. Would prefer not to use all the healing potions, or waste several clips of ammo if there's a more elegant or efficient solution. Sometimes at odds with the butt-kicker, as the tactician likes to bypass a drawn out fight.

The Power Gamer - likes feeling powerful relative to the baseline the game provides, however the game implements this. Often called a munchkin, or min-maxer, but neither is necessarily the case.