I was born in the 1981, allegedly the last year for Generation X, I read about Generation Y and I think what they have going on is more my style.
First system I remember playing is Intellivision. It belonged to my brother, he had an Atari but I don't think he ever let my play it.
The NES is where I officially started I guess. I played Bionic Commando and Rygar over and over. When I finally beat Rygar I ran outside screaming, "I beat it! I beat it!" (I hated that you could never save your game in Rygar). Ducktales and Megaman 3 got heavy play too.
To make the rest of this post shorter....
My favorite game is probably Final Fantasy IV and I can't wait for it to come out on the DS. When I get the DS version I will add it to the SNES, PS1, and GBA versions I own. I haven't beat Final Fantasy V or VIII yet... and I'll have to get a PS3 just for FFXIII I suppose. (I won't apologize for liking Final Fantasy either.)
I skipped out on Nintendo for a few generations (N64, Gamecube, and about a dozen GameBoy variants). I have the GBA Micro, DS, and a Wii.
I spend most of my time on the Xbox360 now.
Currently playing: Ninja Gaiden DS, GTAIV, Mass Effect, Lost Odyssey read