Platformer: I guess Mario probably got me into platforming, though I donno what you'd consider Prince of Persia but I liked that too
FSP: Star Wars Dark Forces
RTS: Can't really remember if it was Age of Empires or the first Warcraft, I was obsessed with both
Point and Click: There was some mickey mouse game, a mother goose game, and later a game called Wrath of the Gods set in ancient Greece
4x: Not sure if it really qualifies but a game called Rise and Rule was kinda my first experience with that, and I became quite infatuated with it
RPG: Final Fantasy and Phantasy Star games, can't recall which was first
Flying Games: There was a really simple game ages ago, I think it was called Red Baron or something. After that I loved playing the Star Wars Rebel Assault games with a joystick
MMO: I honestly can't even remember as I played so many once I discovered them... Everquest, Anarchy Online, some game I can't remember the name of, Asheron's Call, eventually Star Wars Galaxies and Final Fantasy XI... I probably played nearly a dozen of them before I started playing WoW.
City Builder: The Caesar series, beginning with Caesar II though I much prefered III
Really, most of these were when i was quite young so my memory is a tad foggy
