Most of the consoles I've bought weren't for one game, but for the promise of more chances to review games for it in the future. Either that or I got the system as a present. So I'll just list my favorite game for each console I've owned.
Atari 5200: Pengo
Apple ][+: Spare Change
Arcade: Pac-Man (duh) I own one.
80s PC: Zak McKracken and the Alien Mindbenders
NES: The Legend of Zelda
SNES: Final Fantasy 6
90s PC: Lemmings and Jazz Jackrabbit
N64: Banjo-Kazooie & Tooie
Game Boy: Link's Awakening
Game Boy Color: Link's Awakening DX and Wario Land 2
NEO GEO Pocket Color: SNK vs. Capcom: Card Fighters Clash
PSOne: Namco Museum vol. 1 to 5
PS2: Ratchet and Clank series
GameCube: Animal Crossing (but Smash Melee, Metroid Prime, and Kirby Air Ride are so good)
Dreamcast: Marvel vs. Capcom 2
GBA: Astro Boy: Omega Factor
DS: Phoenix Wright series
3DS: Animal Crossing: New Leaf
Wii: Wii Sports
PS3: DuckTales Remastered
Xbox 360: Soul Calibur 4 and 5 and Banjo-Kazooie: Nuts N Bolts
PSP: Loco Roco
Vita: Gravity Rush
Wii U: Splatoon
PS4: Ys 8
Switch: Nintendo Labo
iPad: Animal Crossing: Pocket Camp