I wasn't born in the 90s but I still have played them:
Earthbound
LoZ Majora's Mask
Super Mario 64
Mario Kart 64
Super Smash Bros. Melee
Halo:CE
Animal Crossing
Sonic
(To name a few)
Edit: sorry that it's mostly nintendo but that was what was around
Edit 2:Morrowind and some Pokemon
Edit 3: I've never played a Playstation console so some obvious classics are missing
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Final fantasy VII, VIII, IX