Atari 2600: Combat. Yep, the great granddaddy.
Intellivision: I wanna say the first I played was Utopia, but it was probably actually Space Hawk.
NES: Super Mario Bros. Whee.
Early PC: I played a couple crappy text based games I can't remember (Kingdom?), Inside Trader, and Hillsfar.
SNES: Super Mario World: Of course.
Genesis: Sonic 2. fuck year.
Sega CD: Sonic CD. Wow what a great game that was.
Sega 32X: DOOM. My uncle got me this because I was always bugging him to let me use his laptop to play Wolfenstein.
PS1: RIIIIIIIIIIIIIIIIDGE RAAACER!
Old PC: Diablo II. We got a new computer, I slapped D2 on it, and lost several months of my life.
N64: Mario 64.
Saturn: NiGHTS Into Dreams. I still resent not having my Saturn here to play this sometimes.
Dreamcast: Sonic Adventure. I bought my Dreamcast on 9/9/99 - see comment about resent and Saturn.
PS2:I don't remember, exactly - I'm willing to go on record and say Breath of Fire: Dragon Quarter, though. I don't think that's right, but I bought my PS2 used at a pawn shop, and rented my first game.
XBOX: Halo, dicking around through the first level at a EB demo kiosk.
Modern PC: I'm gonna say Half-Life 2. Again, not sure - there's been a lot.
I'm pretty sure I haven't yet really touched a PS3, a 360, or a Wii, much as I've wanted to.