My early consoles were bought for me by parents but of the ones I bought myself: (And will buy)
Gamecube: F Zero GX, Metroid Prime
PS2: Shadow of the Colossus
Wii: Super Mario Galaxy, Monster Hunter Tri
360: Bioshock
Wii U: Donkey Kong Country: Tropical Freeze, Bayonetta 2, Monolith Soft's X