Significant but not to say all good games:
Full 3D 3rd person action adventure with multiple usable vehicle types - Hunter
Dark top down adventure with mature themes - Dreamweb
Purchased a HD for the Amiga just for the 11 disk swap fest - Indiana Jones and the Fate of Atlantis
Sophisticated 3D combat flight sims - F-117A Stealth Fighter and EF2000
And a special mention to Workbench OS.
The Full Experience
Get an Amiga 1200 with some hard drive space, Install Deluxe Paint, open the KingTut and Venus images in it but don't actually do much painting with it. Go through the install process for something like Fate of Atlantis. Maybe get involved in the Demoscene. Hopefully at some point during your time witness a Guru Meditation. And if there is time left play some Mods in Soundtracker and attach a microphone to a Technosound Turbo 2 and get your Dark Vader voice on.
@csl316 And now a quick Shadow of the Beast 2 death riff, yes?