Interesting question...
I think that the game *most* associated with the Amiga is Speedball 2.
People remember different games as being typical Amiga games depending on the era... it could be Moonstone, Chaos Engine, Worms, Superfrog, Zool, Pinball Dreams/Fantasies - all of them were popular at their respective times.
Other ones that I'd suggest are Xenon and Weird Dreams - as these were featured on one of the Saturday morning UK childrens TV shows ("Get Fresh", IIRC) - very impressive stuff for the time!
There's an Amiga section in the "Retro" magazine this month (or whatever its frequency is; the issue that's in WH Smith now!) which mentions a few of the favourite/famous Amiga games. Can't for the life of me remember what they were, though...