Worms, the original Amiga version. Rated by some the best Amiga game of all time. Also by extension Worms: The Director's Cut, an enhanced Amiga-only release that added a load of improvements and new weapons (Grenade Launcher, Nuke, Postal Strike, Sheep-On-A-Rope, Super Sheep, Concrete Donkey, etc). Worms gives you a great deal of control over the game environment with what we'd now recognise as geomod technology. The game rewards player skill over strategy. The countdown timers improve the game over its predecessor Scorched Tanks, which was very slow and determined and didn't give you much movement. Worms manages to capture much of the irreverent humour of Cannon Fodder, inspired by modern British perspectives on the ridiculous nature of World War 1 trench warfare via war poets whose works were influential in humanizing and de-romanticizing the awful nature of war.
UFO: Enemy Unknown (X-Com: UFO Defense). It's excellent for its gameplay, atmosphere and management simulation. I love how you start out with modern-day technology and must improve by researching new technology and reverse-engineering captured alien tech; that doesn't really happen in the later games and that gives them less of a satisfying grounding in the real world.
Super Metroid. I played this game maybe ten years after its original release and it was still excellent. The progressively improved ability Samus has to traverse her environment is superb. The game's atmosphere is excellent: solitary but not lonely, intriguing but dangerous.
Pokemon Red/Blue. I love this game so much. Even with the new games, the original has a simple and pleasant nature.
Sneech, essentially Nokia Snake deathmatch. An Amiga freeware game, where players control differently coloured dot snakes in an arena and win by boxing opponents in Tron-style. Powerups and obstacles appear at random to keep things interesting. Very well-polished and surprisingly tactical.
Edit: fuck I forgot Master of Orion II. Ikaruga. The Touhou shooters FFFFFFFFF
