Nintendo Entertainment System (NES): Tie between: The Legend of Zelda and Metroid (both were truly innovative and "groundbreaking" during their time, classics in every sense of the word)
NEC Turbografx-16: Ninja Spirit (nearly as good as the "Ninja Gaiden" series on NES)
Sega Genesis: Ghouls N' Ghosts
Honorable mention: Sonic series
Gameboy: Tetris
SNK Neo Geo (Home/Arcade): Tie between: Samurai Showdown series and Metal Slug series
Super Nintendo: Tie between: Super Castlevania IV and Super Mario World,
honorable mentions: Super Metroid, Legend of Zelda Link to the Past, Contra III, Street Fighter II Turbo, and Super Mario All-Stars (one of the first and best "remakes" of classic games)
Capcom Play System I (Arcade): Street Fighter II: Champion Edition
Capcom Play System II (Arcade): Tie between: Marvel Super Heroes and Street Fighter Alpha 3
Honorable mention: X-Men: Children of the Atom
Sony Playstation: Castlevania: Symphony of the Night (the best Castevania game ever made in my opinion)
Honorable mentions: Metal Gear Solid, Tomb Raider series
Namco System 11 (Arcade): Tekken 2
Namco System 12 (Arcade): Soul Calibur
Honorable mention: Tekken 3 (easily the best Tekken game until Tekken 5)
Namco System 22: Rave Racer (technically 3rd game in Ridge Racer series)
Nintendo 64: Tie: Super Mario 64 and Legend of Zelda Ocarina of Time
Honorable mention: Banjo Kazooie (actually better than Mario 64 in many ways)
Sega Dreamcast: Soul Calibur
Honorable mentions: Marvel vs Capcom 2, Tech Romancer, Sonic Adventure series, and Street Fighter III series
Windows games: World of Warcraft (played for a couple of years and for more hours than I would admit to)
Sony Playstation 2: Tie between: Tekken 5 and Gran Turismo 3-4
Honorable mentions: Metal Gear Solid 2-3, Final Fantasy X, Street Fighter Alpha Anthology *note* God of War I & II might rank higher with me, if I were to play through them and had I played them at the time they were released.
Gameboy Advance: Metroid Zero Mission (remake of the classic NES game with new content)
Nintendo Gamecube: Metroid Prime
Nintendo DS: New Super Mario Bros (fun game)
Sony PSP: Tie between: Tekken Dark Resurrection and God of War: Chains of Olympus
Nintendo Wii: New Super Mario Bros. (borrows from everything before it and adds more to make it the best Super Mario game ever created in my honest opinion, highly underrated at Gamespot)
Sony Playstation 3: Batman Arkham Asylum
Honorable mentions: Tekken 6, Marvel vs Capcom 3
Favorite system: Personal Computer, one word "Emulation", in other words Console + Arcade Emulation + PC games = more gaming than time.