One of my favorite co-op experiences on the Amiga was Silkworm. In this shooter game, you play as a chopper or a buggy, or both if you have a friend.
Me and my sister used to play this game for hours, she being the chopper and I being the buggy. The chopper was easier to control, but harder to stay alive. The buggy was stuck to the ground and hard to control, but easier to stay alive since most action happened in the air.
I can't remember that we actually reached the end, but I know that we were damn close. This game and its action got hellish after a while and it was really hard to stay alive. Many good hours spent, and I like the concept of a co-op where the gameplay experience is different between players.