After seeing Galahad's list, I'm beginning to feel rather inadequate ... <sniff!> ...
You mean you're supposed to FINISH games?
Seriously, I think my attention span must be too short when it comes to most games. I was trying to remember which ones I had ever finished (on any platform), and most of the ones I've ever finished were text adventures (especially the old Infocom ones), but I'm not sure I ever finished any of them ON the Amiga. I did finish Space Quest 1 and Leisure Suit Larry 1 on the Amiga, so it's not a total shutout.