The day I bought my Amiga 500 I also purchased two games: Space Ace and Shadow of the Beast. Space Ace was cool especially for someone just coming off the C=64 (the first 3.5" disks I'd ever seen), but Shadow of the Beast made me fall out of my chair. I immediately knew right then and there that my Amiga would need to be connected to my stereo from that point. I had never heard any game sound that cool.
I think one of the games that I played a lot was Pool of Radiance from TSR (i.e. Dungeons & Dragons). One of my favorite games of all time.