Djay's recomentions are pretty good.
If you're into action games, you just HAVE to get the following games:
Ruff 'n' Tumble
Fury of the Furries
The Lost Vikings
All Terrain Race
erm.. I could go on and on and on..
for puzzle games..
Try out Gem'X and Zonked (AKA X-It), 2 great puzzle games for Amiga. Also, Benefactor, The Lost Vikings and Fury of the Furries are half puzzle games too