I'll pick from current gaming categories that I enjoy today:
MMO:
FFXI was my favorite MMORPG, and I really enjoyed it for about 2 years, and logged hundreds of play hours on it. It's getting very stale now, however. I'm thinking seriously about quitting and trying Eve Online.
My wife and I have played MMOs forever... I logged way too many hours in "Neverwinter Nights" (Yeah, the original one, on AOL, when you paid by the hour to play on AOL, YIKES!) and DarkSun Online. Both were excellent at the time.
Space Sim:
Freelancer for sure!
RTS:
Warcraft, Starcraft, Command and Conquer, and Sid Meier's Alpha Centauri all in a 4 way tie.
RPG:
Tough category for me, I have played RPGs for as long as I've gamed.
Ultimas, Gold Box SSI games (all of em), and Wasteland all come to mind as the top of this category.
Surprisingly, none of the recent RPG titles, with the exception of NWN/NWN2 has even mildly interested me. I've tried to enjoy many of the other titles, but they just don't play as well any longer. I think I'm too into the online gaming now to allow these single player games to garner much of my interest.
Runners up/Honorable Mention: The Sims 2, Final Fantasy 7, Final Fantasy 12.
Games I'm actually waiting for/wanting to try: Eve Online and Spore.