The 1st Amiga game I ever played was Wings of Fury. I already said that in the "1st amiga game you ever witnessed" thread
When I got my Amiga, I got lots of disks with pirated games, and I believe the 1st one I runned was R-Type 2. I never bought any original Amiga games, because here in Brazil, this was something stupid to do at that time.
The 1st PC game I ever played was... Wolfestein 3D, I believe. The 1st one I played on MY PC was probably Stunts. Or Theme Park, I am not sure. Anyway, I think Theme Park sucks, while Stunts I still keep playing it today.
The 1st PC game I bought original was.... let see if I can remember .... Rebel Assault II , I guess. Unlike most people, I like that game a lot, even although it's just a shooting galery with great gfx and sounds. Maybe it's because I love Star Wars. or the atmosphere, I don't know. But I already had MDK original, it was a gift from a friend.
The 1st game I runned in an Amiga Emulator (DOSUAE ! anyone remember that? ) was The New Zealand Story. I was just SOOOO happy to see an amiga game running on my PC (It was my 1st try to emulate anything on PC.)