Discovering Dungeon Master at my local dealer on the day of it's release, then actually playing it and being absolutely blown away. Then, to top it all off, a week and a half later finishing it. Probably the single best (single person) gaming experience I've ever had.
Settlers, CIV and SimCity were also great on the Amiga, I pissed weeks of my life away playing those..., but Dungeon Master just stands out above the rest in my memory.
The next great gaming moment for me was when I discovered Betrayal at Krondor on the PC - from that point on I was hooked on PC games. (Please no flames, I'm sure that game by itself cost me 20% on my university grades that semester

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