I don't like RTS games at all, but had some good fun playing Total Annihilation with friends in college.
While FPS games aren't something I play very much anymore due to their ubiquity crossed with their lack of innovation, I do have some fantastic memories of DOOM 1 and 2, and Unreal Tournament. Half Life 2 Episode 2 was pretty good too...
Rhythm games aren't usually my thing but I enjoyed Theatrhythm (for obvious reasons), DJ Hero 2 (for even more obvious reasons), and the Project Diva series (for yet more obvious reasons).