Board game: Monopoly. Second place: Life.
Card game: MTG, card and the Steam version.
Digital, by genre:
RPG: Baldur's Gate. Second place: Diablo II. Skyrim is, thus far, a distant third, but it's only a matter of time because Skyrim is new.
PvP, 2D: Mortal Kombat 3 (version w/all chars)
PvP, 3D: Guild Wars (signed up to be considered for GWII beta)
FPS: Left 4 Dead 2. I love this game and play it weekly. A close second in time played is the whole of the Half-Life 2 series.
Puzzle: Any Myst game. That shit was dope, and tough as nails. (There's supposed to be a movie coming out soon).
Strategy, real-time: Starcraft II. Command & Conquer 3 is a close second in time spent.
Strategy, turn-based: This is a tie between Civilization V and Galactic Civilizations II. While Civ V has the polish and production values one would expect from a series of its pedigree, and is a great deal of fun, Gal Civ II is staggeringly intricate and has the look and feel of a (if you wish it to be) massive board game. I've spent about the same amount of time on both.
Indie: Minecraft, easily.
I'm sure there are other genres I'm not thinking of at the moment, so that's a partial list. I think I'm going to go play something.