Coming from someone who bought most of their consoles later in life, I can only do a partial assessment of this.
Mega Drive/Genny: Sonic 1 (pack-in game FTW!). I still remember going to Wal*Mart and getting the Genny. And I was like, 2 years old. And it was my oldest memory. Sad, isn't it?
Master System (bought 2 years ago): Sonic 2.
Game Gear (bought 3 years ago): Sonic 2 (I have a rather unhealthy obsession with the 8-bit version of Sonic 2).
Game Boy Advance: Super Mario Advance. Or, more truthfully, Pokemon Gold (200 hours of my life are in that game).
Saturn: NiGHTS...Into Dreams
N64 (bought used, about 3 years ago): GoldenEye 007
Playstation: Need For Speed III.
Playstation 2: Grand Theft Auto: Vice City.
Dreamcast: Sonic Adventure.
Sega CD (bought 2 years ago): Lunar: The Silver Star.
Sega 32X (bought 3 years ago): I'll get back to you on that on Friday. I want Chaotix, however. Badly.
Neo-Geo Pocket Color: Sonic Pocket Adventure.
Game.Com: I dunno what I was thinking.
SNES (bought 2 years ago): Super Mario All-Stars
NES (bought 3 years ago): Ghosts 'n Ghoblins