Amazing Games:
Elite - Best game ever as I've said
Final Fantasy 7 - Best RPG ever hands down, and I've played some great RPGs like Baldurs gate and co.
Golden Axe - No more need be said
Double Dragon 1 + 2 - The big guys that kick you over in 1 kick were the best, they looked like they were on heroin or something too! Double Dragon 2 is probably the best 2-player co-op game ever, just for 2 player mode B where you could beat the shit out of each other.
Streets of Rage - Totally agree with Avernus on that one
Street Fighter 2 - Pure genius
Super Mario Kart (Snes) - Best racing game ever by a mile, and I was soooo good at it.
Probotector NES - Great game and I was amazing at it
ISS Deluxe PS2 - Okay so I know Pro Evo and all is better, but I loved this game because I was so fuckin good at it
Super Mario 1,2,3 + World - Best platformers really
Wipeout 2097 - Great racing game, once again I was sooo good at it.
Halo 1 + 2 - Halo 2 best online game
Marathon 1,2,3 - Precursors to Halo, and in some ways better (edit: also, Marathon on Legendary level is probably the hardest game I've ever played, I never got past the first level)
Civilization 1,2,3 - Best strategy games ever
Warcraft 2 - Great game, Warcraft 3 was great too but I love Warcraft 2
Escape Velocity + sequels - Shareware game on Macintosh, kinda like a modern day Elite, really really really good fun.