My list is probably predictable, but I have a couple of oddballs in their as well:
1. Final Fantasy 7 - some people dog it now, but I have never been more enthralled in a game in my life!
2. Metal Gear Solid - holds up remarkably well all these years later
3. Castlevania SotN - still great after all these years!
4. Tekken 3 - surpassed by sequels, but at the time, I couldn't put it down
5. Ape Escape - still my favorite non-Mario 64 platformer from that era
6. Tomb Raider - the first, and still the best in the series (though I loved 2 as well)
7. Ace Combat 2 - the best flight-based game of the era
8. Gran Turismo - I picked the first because, even though 2 was better, the first was so mind-blowing when it released
9. Syphon Filter - Despite some rough edges, still one of my faves.
10. Wipeout XL - I loved playing this game until the wee hours of the morning
There are so many other faves I had as well (Jumping Flash, Einhander, Alundra, Moto Racer, Oddworld, One, etc) that I will disagree with my own list ten minutes after I posted it.