Escape Velocity (Override/Nova) - I'm a big fan of sci fi, and it's great to just explore the universe. Buying new ships and upgrades is also very much like spending character points in an RPG, so it's doubly fun. Also, every time I try any game that's in the same genre, I always come back to EV being better. Ambrosia got it so right that they haven't bothered to make a sequel to Nova and nobody else has been able to best them.
-Honorable mention in this category is Wing Commander: Privateer, but the campaign was too short and it lacks replayability. X2/X3 might also come in if I can actually get them to work.
Unreal Tournament (2004/III) - When I originally got the UT demo with just 4 levels, I played it far more than any other full version game I owned. Buying it was a no-brainer. Since then it has still been my favourite FPS, and I doubt anything will replace it. It's in my blood, no matter how long I go without playing it I'm right back in pulling off non-scoped headshots while flying through the air.
-I can't think of anything that has almost dethroned it. Multiplayer FPS just doesn't get as good as UT, although I think 2004 is probably the best of the bunch.
Descent (2/3) - 360 degrees of freedom in all 3 dimensions, moving exactly how you like. The soundtrack is also just awesome, and I enjoy listening to it without the game as well. It's a shame it hasn't been done since, and I'm eagerly awaiting Descent 4, if it ever comes out.
-Honorable mention to Forsaken, obviously. Not like there's anything else.
Deus Ex - FPS, stealth & RPG all in one. Plus I'm a cyberpunk fan. Unreal Tournament is king for multiplayer FPS, and Deus Ex is king for single player. I'm cautiously optimistic about Human Revolution.
-Honorable mention to Klingon Honour Guard (I'm a Trekkie) and Thief: The Dark Project.
Persona 3: FES - As far as RPGs go, this is the best. The story is interesting, and it actually has a mechanical benefit to social interaction, as well as an interesting time management element with actions going on a day by day basis. It actually feels like you're playing the role. It also still has the fun aspects of most RPGs in having an interesting shortcut to make you more powerful. In this case it's all about taking on the boss battles solo.
-Honorable mention to Final Fantasy X, having played FF1 I didn't care much for the series, but FFX got me back into Final Fantasy and from there into JRPGs in general, leading to Persona 3.
Also, I have to make a shout out to Minesweeper!