For Sega Genesis - I remember the Sonic Games, as well as Dune: the Battle for Arrakis.
I never owned a Super Nintendo (blasphemous, I know)
For PSX, there of course were the Final Fantasy and Parasite Eve games, as well as this 1 game I played over at a friend's house which name escapes me (It was a point and click where you play as a talking dragon in a mid-evil era, where you are trying to become a knight)