Some of you have already mentioned some favorites of mine, so I'll just list some that have yet to be listed.
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Wizball still remains a favorite to this day. Aside from the absolutely gorgeous, enchanting music, the creativity on display has barely been matched by any other form of media in my opion.

Mad Doctor: An open-ended sandbox game where you are free to obtain body parts in any way you desire in order to make a Frankenstein-esque monster? Before it's time.

Head Over Heels: Much like Wizball, the imagery in this game was like crack to my
imagination.

Skate or Die: I'll chalk this down to nostalgia. It is a very good game, however.

Parallax: Again, this was rather ahead of it's time. It's combination of Space Combat and adventure elements makes it stand out:

Pitstop II : It's a racing game; first and foremost, but the inclusion of the Pitstop adds a level of tension and urgency (and yes; strategy) that remains unmatched even today.