Earthbound!
A lot of the greats have already been mentioned by others, but Myst (1993) and Riven (1997) deserve to be up there.
Not only for the immersive worlds you got to experience through masterfully crafted imagery, sound and music, but also combined they held the record for best selling game series until they were surpassed by The Sims.
PC: Descent. Full 6 degrees of freedom movement. Fantastic.
In no particular order, these are the games I played the most back then.
SNES
- Super Bomberman II
- Stunt Race FX
- Super Mario Bros
- Yoshi’s Island
PS1
- Gran Turismo 2
- Spyro 1 & 2
- Crash Bandicoot series
- Twisted Metal 2, 4
- Jet Moto series
- Coolborders series
- Pro Skater series
- Einhänder
PC
- After Dark Games
And a couple of nearly-90s favorites,
PC
- 4x4 Evo 2
- Red Alert 2
- OG Halo
There are so many… Here are some that I probably spent the most time with:
- Master of Orion
- XCom (the original)
- unreal tournament
- Elder Scrolls Daggerfall
- Falcon 3.0
- Mechwarrior 2