Donkey Kong Country series
I have mixed feelings about including this one on the list of top co-op SNES titles. It's easily one of the best games available on the system, and in fact the entire series was groundbreaking and innovative in a variety of ways. The graphics and gameplay are peerless on 16-bit systems. However, the co-op is lacking. Control is shared tag-team style between DK and Diddy, so you never really have both players acting at the same time. It's still fun, it's just not ideal. Still, Donkey Kong Country and its two sequels are among the highlights for the Super Nintendo.
Perhaps no other series is as embedded into the brain of the 90s gamer than NBA Jam. The arcade-style take on NBA basketball was ingenious, and the over the top action brought a smile to your face, even if it was the CPU dunking right over you. The announcer's catch phrases, like "He's on FIRE" and "From DOWNTOWN" are likely still heard on neighborhood courts to this day. The SNES version of NBA Jam allowed two players to team up against the AI, though due to legal reasons Michael Jordan and Shaquille O'Neal were left off the rosters. It didn't matter though, since you could play as Bill Clinton and Al Gore!
Secret confession: I consider myself a fan of JRPGs, but I've never played Secret of Mana. I feel better now that I've got that off my chest. Well known for it's excellent story, real-time battle sequences, and an influential menu system, the game is fondly remembered by many. Very unusual for the genre, Secret of Mana includes co-op, and it does so in a particularly innovative way. Extra players can simply plug in a controller and take over a character. Yup, this is true drop in/drop out co-op. This is something many modern games don't get right, and Secret of Mana did it perfectly in 1993!
I've gushed about Turtles in Time before, but it still deserves mentioning in any list of SNES co-op classics. The turtles go on a rollicking adventure throughout history, from the age of dinosaurs to pirate ships and even into the far future. The Super Nintendo version only allowed for two players, but it was arguably better than the arcade counterpart, with bonus levels and a revised final battle against Super Shredder. Throwing Foot clan ninjas out at the screen was a nice way to show of the SNES' awesome Mode 7 graphics and never got old.