Atari 2600: Kangaroo (I wore the B&W TV down after a 15-hour marathon trying to reach the top of the third stage; melted the cables inside the TV cabinet).
NES: Super Mario Bros.
TurboGrafx 16: Blazing Lasers.
Atary Lynx: S.T.U.N. Runner.
GameBoy: Tetris.
SNES: Yoshi's Island: Super Mario World 2.
Genesis: Contra: Hard Cops.
TurboDuo CD: Dracula X.
3DO: Road Rash.
PlayStation: Resident Evil 2.
Sega Saturn: NiGHTS... Intro Dreams (with Sonic R a very close second).
Nintendo 64: Super Mario 64 (lame selection but back in the day no other 3D game could touch the magic this Miyamot-designed masterpiece still has). Honorable mentions to Mario Kart 64 and Goldeneye 007 for the obscene hours of multiplayer spent playing with friends.
Virtual Boy: Wario Land.
GameBoy Color: Pokemon Puzzle League (same as Tetris Attack for the B&W GameBoy but with a Pokemon license attached).
NeoGeo Pocket Color: Capcom vs. SNK: Match of the Millennium.
Dreamcast: Resident Evil: Code Veronica.
PlayStation 2: Hot Shots Golf Fore!
XBox: Halo (stayed up late playing more than any other game, to the point me and friends had to coordinate vacations so we could stop showing up late and dead tired at work the following day).
Gamecube: Resident Evil 4.
GameBoy Advance: Moto Racer Advance (best portable racing game nobody has ever seen or played, but I have!
).
N-Gage: Colin McRae Rally 2005 (honorable mention to Tomb Raider, an oldie but still an excellent goodie in portable form).
Nintendo DS: Ridge Racer 64.
Sony PSP: Hot Shots Golf! Open Tee.
XBox 360: Call of Duty 2.
Don't have a Wii or PS3 yet. I also want to say that coming up with just one game for each system is freaking hard. I had five games for each system that could have been my choice, and only by some personal bias did I come to name one over the others. What I'm trying to say is... NOT FAIR!!! 