Unreal Tournament (Also UT 3, and the now 'never to be sufficiently finished' Unreal Tournament). Quake III Arena was always a good time. Battlefield 1942 for its variety.
Never really got into modern shooters too hard. I always feel the sameness in weapon choice with little distinction and every player min/maxing for the best weapon mix. When I do play modern titles, I do silly things like run scopeless bolt action or semi auto.