RTS: The best I've played is probably Starcraft 2. I am rating these for single player campaigns, and SC2 just has far more veriety and imagination than anything else. For total amount of fun gained, Age of Empires 2 or SpellForce.
TBS: For the wargame side of these things, Warlord 3: Darklords Rising is excellent. Simple, fast-paced, not too much busywork, and plenty of skill involves. For the 4X side of things, Civilization 4 is probably the objective best game, but Civilization 2 gave me more fun, and I can play a game of Civ 2 much more quickly which I like.
Grand Strategy: Hearts of Iron 2. One minute I am securing my oil supplies. The next managing my production lines. The next I'm co-ordinating an assault on Moscow. Then I'm dealing with the fact that my attack on Gibraltar has fucked up because of a random snowstorm. This game can hurt to play, but in a good way.
FPS: Thief: The Metal Age. This is pretty much the perfect Thief game, which is pretty much the perfect action game. I enjoyed Dark Project more because I played it first and I played it a lot, but Metal Age is definitely better. If you want an actual shooter, then probably CoD2, but I don't like shooters much. I do like the bits of CoD2 where you're a guy in a big battle.
RPG: Baldur's Gate 2. This is a wonderful game with loads of fun quests, fun characters, fun spells, lovely graphics, amazing encounters. Definitely my favourite game of all.
Action-RPG: Vampire: Bloodlines. Because vampires.
Casual: Puzzle Quest or Audiosurf. Unbelievably addictive games. I thought Puzzle Quest was just a joke, played the demo for a laugh, couldn't stop.
Sim: Railroad Tycoon 2. This is a hard category to judge, there are some games i really love like SimCity 2000 and Capitalism Plus, but I like trains a bit more.
Other games that I don't know how to classify: Terraria and Duels of the Planeswalkers.