I think I'll switch this up and give my favorite games from each individual system I've owned or just played:
PC - Baldur's Gate II: Shadows of Amn
Arcade - Golden Axe
ColecoVision - Gorf
Atari 2600 - Combat
NES - Super Mario Bros.
SNES - Super Star Wars
Sega Master System - Alex Kidd in Miracle World (an unassuming platformer...but I dreamed about it when I slept).
Sega Genesis - Phantasy Star II
Sega Saturn - World Series Baseball
Nintendo 64 - Goldeneye
PlayStation - Final Fantasy VII
Dreamcast - Phantasy Star Online
PlayStation 2 - Baldur's Gate: Dark Alliance
Xbox - Star Wars: Knights of the Old Republic
Gamecube - Resident Evil 4
Xbox360 - yeah, I know, a little early, but so far it's Elder Scrolls IV: Oblivion
PC - Baldur's Gate II: Shadows of Amn
Arcade - Golden Axe
ColecoVision - Gorf
Atari 2600 - Combat
NES - Super Mario Bros.
SNES - Super Star Wars
Sega Master System - Alex Kidd in Miracle World (an unassuming platformer...but I dreamed about it when I slept).
Sega Genesis - Phantasy Star II
Sega Saturn - World Series Baseball
Nintendo 64 - Goldeneye
PlayStation - Final Fantasy VII
Dreamcast - Phantasy Star Online
PlayStation 2 - Baldur's Gate: Dark Alliance
Xbox - Star Wars: Knights of the Old Republic
Gamecube - Resident Evil 4
Xbox360 - yeah, I know, a little early, but so far it's Elder Scrolls IV: Oblivion