Primarily strategy games. Shooters like Doom, Duke Nukem, Shadow Warrior, Half-Life and Unreal Tournament came later for me. These were the ones I played in my early years:
1996: C&C Red Alert + Time Commando + DX-Ball + SimPark
1997: Age of Empires + Theme Hospital + Dungeon Keeper
1998: Dune 2000 + StarCraft + Need for Speed 3: Hot Pursuit
1999: C&C Tiberian Sun + Heroes of Might and Magic III + RollerCoaster Tycoon + Grand Theft Auto 2