Starcraft, for the sheer cutting-edgeness of having 3 different races.
Startopia, a GREAT game to play through once, but unfortunately not much replay value.
Warcraft III, no need to explain I don't think.
Diablo II, See above.
Unreal Tournament, for being so readily moddable, and for upping the stakes in terms of online play.
Quake III Arena
BF:1942, gotta love a vehicled war game with such a great mod as Desert Combat.
Wolfenstein: Enemy Territory, for it's great play and simplicity.
PS: Doom 2 was released way before 96, as were: Star Control 2, Quake, Warcraft II, and Master of Orion 2...