In no order...
Geoff Crammond's F1 grand prix (Amiga)
Me and my mate would love how you could take turns at controlling every driver in the race. We'd rename EVERY driver to have stupid names like "Blind man" and basically roleplay a reason as to why said driver decided to drive as fast as they could into a wall and have a spectacular crash. Except the two drivers with our names on that would win 1st and 2nd place.
Little Computer People (C64)
It was so new at the time to have just a man in control of his own actions, walking around a house inside your computer. Then stopping his food from being delivered and letting him literally go green. He never dies though.
SEUCK (C64)
Okay so not a game per say, but I would just love to be able to play all the games I'd made on that. (Shoot em up construction kit)
The Amiga version s(e)ucked though. I mean, no collision detection system? Pants!
Creatures 2 (C64)
Again, I have good word it sucked on the Amiga, but the C64 version was a classic. Fiendish challanges and puzzles, and I learnt the word bugger from that game too.
Colonization (Amiga)
For some reason, I just can't bring myself to sit down and play these kinds of games anymore, but I spent many hours on this great game. I never did 'win' it though, despite my efforts. I also bizarrely loved the music it played.