For me there were a lot of great Amiga games, as there are for many others too. Here are some of my favourites.

Frontier: Elite 2 This is probably the game I played the most out of any game on the Amiga. Based on the original classic Elite it expanded the games universe and added a lot of new features. Space trading, combat, missions, assassinations... as well as bringing the game fully up to date with filled polygon graphics and great classical music score. An amazing game.

Dungeon Master Originally released on the Atari ST, this game was responsible for the video game RPGs moving out of the Text Adventure era and into the visual interactive one.

Eye of the Beholder 1 and 2
Building on the Dungeon Master style of gameplay it expanded on the ideas it introduced, including AD&D rules and creatures from the AD&D universe. If you like RPGs this was one of the best on the Amiga.

World of Legend The sequel to Legend, this RPG uses a similar dungeon crawling isometric style to Heroquest and a map based world view to travel.

Populous 2 The sequel to Populous, this is still one of my favourite God games released to date.

Sim City 2000 The first Sim City was released for the Amiga before any other platform, but although this sequel was released on the PC first, the AGA Amiga version was the version I originally played and it is still my favourite version in the series.

Arkanoid II There have been a lot of Bat and Ball style games released over the years but this is still my favourite.

Alien Breed SE '92 A brilliant sci-fi above view Alien themed shooter, with this special edition polishing the original with some little tweaks and additions.

Wings For many this is still one of their favourite games. Taking an arcade approach to flight sim style gaming, it mixs many different styles of bi-plane flight into this great game, with the diary entries between each level adding a lot of atmosphere to the game. Foremost an Arcade Shooter, it contains some great 3D flight missions as well as isometric levels.

Lemmings Given away in a lot of Amiga A500 and A600 packs, and for good reason. It is still one of the best puzzle games and is still as fun now as it was on release. The sequel Lemmings 2: Tribes added a lot more themed and interesting levels to the gameplay.

Chaos Engine From the Bitmap Bros this great shoot 'em up played it's best in Two player mode. Steam punk style design with great sound effects and level design.

Speedball II A brilliant futuristic sports game based on ideas from the file Rollerball, mixed with ideas from Football and American Football. Still only of the most playable and enjoyable sports games to date.

Flashback Games before it had used retroscoping to animate their game characters (Prince of Persia) but Flashback really did this well. It also included a great story and many different things to do in this platformer that made it more of an Adventure than just a standard platform game.

WolfChild A great arcade platform game.

D/Generation This is one of my favourite Arcade Adventure/shooter style games on the Amiga. Using an isometric style it has some great puzzles in each area and always brings back memories of some of the games on the 8-bit platforms such as Knightmare.