I've always considered Dungeon Master the best Amiga game ever (and yes, I finished it a few times). It's atmosphere is like nothing else. I liked the sequels as well (although I never did finish DM2).
Lotus Turbo Challenge 2 was a fun multi-player game. So was Wayne Gretzky Hockey. Loved pulling the goalie when he had posession of the puck - the extra attacker would come onto the ice but the goalie takes the puck with him so game play continues without the puck and all the AI players go mental! :-D
Populous and Power Monger were also amazing games, spent many hours conquering virtual lands and people...
Of course, I think the first game I ever played was Marble Madness, so I suppose I should mention that. Other great classics include Menace, Barbarian, Fire Power, Speedball, Turrican, and one of my all time favorite shoot-em-ups: BattleSquadron (which I finished several times)!
- Mike