Earthbound.....man,i only played MOTHER 2, but i must say that this shit is amazing.
also, giygas is a creepy boss, but interesting at same time.

Added.

also, have you ever played Cadillac Dinosaurs? it's a good beat-em up arcade game.
but from arcade my favorite game is Killer Instict, an BADASS fighting game, it was launched to SNes too.