How hard is it for some of you people just to check first before you post? 90% of the games suggested so far are available on other systems. Just go to Lemon Amiga or Hall of Light (
http://www.lemonamiga.com and
http://hol.abime.net ) and search for the game you THINK only came out on the Amiga, and you'll most likely see that it's also on the Atari ST, PC, Mega Drive, or a bunch of other systems.
As for my favourite Amiga-ONLY games, here's a short list:
Fightin' Spirit
Ruff 'n' Tumble
Mr. Nutz: Hoppin' Mad
Agony
Banshee
Lionheart
Disposable Hero
Shadow Fighter
Breathless
Kid Chaos