Hmm, this is all subject to change:
Atari 2600: Yar's Revenge
NES: Super Mario Bros. 3 - Tanooki Mario pwns all.
Genesis: NHLPA 93 - Changes made in 94 were not for the better, set back the franchise years.
SNES: Super Mario Kart - None of the follow-ups have been as fun to play as the original.
PS1: Resident Evil - Awesome game, first game that truly introduced horror to the genre.
Saturn: Virtua Fighter 2 - Excellent arcade port
Dreamcast: NFL 2k - Have never looked at the Madden series of games the same since.
PS2: GT3 - Haven't played 4 because I used up all my accrued sick time playing 3.
GameCube: Viewtiful Joe - An homage to the simpler days of gaming, sorta.
Xbox: KOTOR - I loved this game so much, I've played it 4 times, despite having done all the quests, side quests etc. The disaster that was the second still disappoints.
GameBoy: Pokemon Yellow - Why play Red or Blue when you can have Pikachu from the get-go?
Arcade: Street Fighter 2, Champion Edition - Ken > Guile, nuff said.
Intellivision, Colecovision, Sega Master, SegaCD, 32x, 32xCD, TGFX-16 and 3DO all sucked badly and had no games worthy of mentioning.