With memories of some early PC gaming experiences:
FPS: Operation Flashpoint (while I gringe to put it down on a level with the usual FPS' - prob. better in Simulation), about two weeks ago finished Farcry; started in this genre with Wolfenstein 3D, Doom, ...
Strategy: War in the Pacific (turn-based); fond memories of Panzer General, Warcraft, History Line 1914-18, Dune, Warlords, ...
Sport: I have a FIFA manager but it didn't manage to get on my new PC yet (~3month); actually played barely any sport games...
Online shooter: I sometimes consider to give Americas Army another try, but I might instead go back playing some OFP Coops...; I bet nobody knows a game called (nc)snipes (IIRC) played on a Novell Netware LAN (late 80ies)
MMORPG: Navyfield (but not for a month or two); for a very short time I tested Ultima Online (as a player of some of the old Ultima series)
Simulation: Silent Hunter 3, IL2; still remembering Silent Service, Red Baron, Battle over Brittain, Task Force 1942, Aces of the Pacific....
RPG: for a long time M&B is the first of it's kind; in the ancient days I liked to play some Ultima episodes, Eye of the Beholder I&II, Fallout 1&2
Edit: Didn't know that it was a piece of computer gaming history,
SNIPES:
When you play Snipes, know that you are holding a small piece of history in your hands. Not only was it one of the very first network applications ever written, it is also the ancient precursor of multi-player games like Doom and Quake that are so popular today. They may not want to admit it now, but I am quite certain that Drew Major and Kyle Powell played the world's first over-the-network "deathmatch" with Snipes, ...