That depended entirely on the game. Most RPGs had some sort of save feature, even the old Final Fantasy on the NES. On the SNES, Super Mario World, the 3 Donkey Kong and Super Metroid all saved your game, instead of relying on passwords.
I'm the autist but you single out games to make my statement invalid? Like it wasn't a thing back then that games didn't have a proper save feature haha