Online FPS: Quake (especially with CTF and Team Fortress!)
Lan FPS: Duke3D
Single Player FPS: Half Life (Team Fortress Classic made this great for online play too though ...)
4X: Alpha Centari was fvckin great! Awesome single player or multi player.
RTS: Total Annihilation, my favorite RTS by far.
RPG: I'm gonna say Fallout here. It was really quite awesome. Fallout 2 as well, since it was nice having the car hehehe
Economic: Transport Tycoon Deluxe was my favorite, even liked it better than all the simcity games and railroad tycoon.