I think that one of the Amiga's strengths was its variety of games that represented many different genres.
For example, there were PC type point and click adventures (Monkey Island 1&2), original genres (Populous, Dune 2), cutesy platformers (Rod Land and Qwak), fun racing games (Micro Machines, Nitro, Lotus), deep strategy games (Civilization), hardcore RPGs (Ultima VI), shmups (R-Type 1&2), highly polished shoot-'em-ups (Stardust, Banshee), Wolf 3D & Doom clones (Gloom, Alien Breed 3D), arcade beat-'em-ups (Shadow Fighter), 8-bit beat-'em-ups (IK+), highly complicated simulations (Tornado, Shuttle), puzzle games (Gem'X), footy games (Kick Off 2, Sensi Soccer), virtual world games (Damocles, Hunter)...
In addition to all of this there are loads of multi-genre titles e.g. Turrican, Moonstone etc. and a highly inventive shareware/freeware industry.