Then that was the Shinobi games, Strider, Ghouls n' Ghost are the ones that come on the top of my head (I think Sonic broke Sega, that level of success made them a much worse company, and it was never that good... maybe Sonic 2, but no other Sonic game is truly great).I liked the Megaman games too. MM3 being my favourite, but MM1 was one my first games I played in my memory. My brother is a way bugger Megaman fan than me though.
How about on 16-bit?
I did not have a SNES back then, but I managed to try a few games.
All in all I have always preferred JRPGs, "adventure games where you explore", schumps...