Exclusives mainly.
Sega Megadrive - Sonic, Castle of Illusion and World of Illusion.
Dreamcast - Sonic Adventure, Shenmue, JSR, Crazy Taxi.
Gameboy Colour - Pokemon.
Gameboy Advance - Loved the GBC, so bought this one too.
Nintendo DS - Got it as a present.
Gamecube - Zelda and other games. Tbh I can't remember much about the console, didn't care for it much.
Playstation - Mostly third party exclusives; Metal Gear Solid, Tekken, Final Fantasy VII plus a load of other great games.
Playstation 2 - Same the the above, with followup games/titles.
Playstation 3 - Most diverse library of games plus lots of console exclusives not available to get on PC.
PSP - Portable PS games, awesome.
Xbox - Halo.
Xbox 360 - Halo 3 and Alan Wake. Plus, I got pressured into getting one for COD4 -_- (what a mistake that turned out to be).
Also, why are people bringing up PC when OP specifically asked about consoles?