Roughly chronologic (with exeptions when themed summarization seemed suitable), not refering to publishing date but when I first played the games:
1. Mercenary
2. Elite
3. Cholo
This is the Triad of mighty 3D-games on the C 64 (my first computer) that impressed me enormously. Another thing all three titles have in common is their nonlinear gameplay (to different extent). I must say Mercenary impressed me more than Elite at the time, whereas I spent much more months in the latter simply because it had that clever feature of being open ended. And of course there was that strange ambition to reach the Elite-status. In hindsight I see the things I had to sacrifice in order to reach that aim (double meaning intended), so should I rather have experienced more friends, better performance at school or a teenage first love for the price of not being able to call my self an Elite-pilot? - I guess you hoped for that you lazy docking-computer-users without a clue how to kill pirates using side-mounted lasers!
4. FE2, FFE, X, Orbiter
Seems I like space sims.
5. Dune II, Mankind
My most fondly remembered experiences with real-time strategy games, Dune II being the introduction to the genre for me, still in 2D on the Amiga, and Mankind being an early and brilliant effort to make a 3D-RTS-space-MMOG that got me hooked even longer than Elite (but only because there was no MMO-version of Elite).
6. Battle Isle III
The best turn-based strategy game I ever came across and the only other game that succeeded in ending up in my list without 3D graphics (apart from short playbacked battle sequences - quite original and very well staged actually). Includes the best Midi-music I ever heared - sounds great with a good wavetable.
7. Mechwarrior Series, Star Siege
How could one not fall in love with robots the size of skyscrapers at ones fingertips?
8. Tomb Raider Series
I really liked TR I-IV, and V-? are the only singleplayer games I might consider spending reasonable time on in the future. But it would be great to share the experience with at least one other person in front of the screen, rotating on the controls. If there has ever been a game where the fact of four eyes seeing more than two could be used to great advantage, this is it.
9. V 2000, Infestation
Mentioned together because of the similarities in gameplay and aesthetics. Very creative, weird and atmospheric stuff. I think I did not finish both of them, and I must admit I feel some urge to do that right now. Again, it would be great to have another enthusiast in front of the screen to share the experience.
And of course there are the PC-ports of the two sequels to Mercenary (Damocles, The Dion Crisis) and the remake of Cholo in Tron-like graphics. Perhaps I should put together a retrogaming club to get rid of that dreadful singleplayer element in singleplayer games.
10. Jumpgate
Space-Sim-MMOG with twitch-based combat and realistic physics - enough said. Loved it for a few days some years ago (not longer because I felt I had obligations in Mankind) and for two months more recently and will probably come back to it as soon as I find a replacement for my broken joystick. I also tried to buy TrackIR on Ebay but that's not home and dry yet.
I know, I cheated a little bit in order to sneak in some more than ten. (-;