Since people here have mentioned szome of my favorite games like point and click adventure games ill say some not mentioned.
Moonstone: A hard days knight - Superb game, loads of fun and even multiplayer.
James Pond 2, robo cod - This game has given me loads of hours.
Tearaway thomas - Not everyone likes the high speed, but I love this one, keep you on your toes and work on your skills.
PANG - This is a aweasome game to play with a friend, you will love and hate each other
Dune 1-2 - Needs no explanation.
Syndicate - Nice game but not for everyone.
Another world - Great game, hard sometimes and it has a nice intro vid.
Flashback - Somewhat like above game but looks alot better.
Prince of persia - No need of explanation.
Arabian Nights - Underused gem, people tend to forget about it, but it's an nice looking platformer with decent controls.
Ruff 'n' Tumble - Nice little game, feels a bit like a more simple version of metal slug.
Toki - Many would not agree with me on this one, but I like to be a human transformed to a monkey with oversized head whos goal is to find his love taken by a "huge hand"!
Project X - Great Shmup without any doubt at par with
R-Type
Swiv - Needs no explanation.
I could keep writing forever since I love a LOT of games for the Amiga.
EDIT: forgot to mention Silk worm after swiv! Great for 2 players.
There is also a bunch of good RPG's for the Amiga that I love.