I had an old Amiga 500 or whatever it was back in the day, handed down through the family. (so when everyone was playing their megadrives, SNESes and later, ps1s amd n64s) I was bashing away on the classic floppy disc games of the Amiga...
good times :)

some of my favs:

Cannon Fodder
We all know this, classic!
war! never been so much fun!

Flashback
the graphics were amazing to me and still are for the format,
loved the realistic movements too.

Alien Breed
creepy music and scary aliens. well, at the time.

Silkworm
fantastic two-player-arcade-joystick-action on this :)

Sensi Soccer
More multiplayer goodness :)

Turrican 2
great guns and weird alien thingys. funky tunes.

Chasos Engine
great co-operative fun with a friend.

Galaga Deluxe
Stupidly addictive, that is all.

Monkey Island
can't rememeber which one i had, but great fun :)

Name yours...