Secret of Mana, Super Mario Kart and Turtles in Time were my favourite coop games back in the days.
For solo play, nothing beat a good round of Prehistoric Man while everyone else was playing Donkey Kong. Not that Donkey Kong is bad, it just does not feature a screaming caveman with beerbelly
These are all on SNES ofcourse. Everyone knew that the Sega stinks
PS If you haven't played it already on some other system, go play Legend of Zelda: a Link to the Past. Best. Game. Ever.