Mario is in Punch Out!!. Just sayin'.
Anyway, I'd have to think a lot for this one, but here are some titles that took up a huge amount of my time. They may not have been good at all, but for most of that era I didn't read the magazines, so I didn't have a means of figuring out what the cream of the crop was (random purchase algorithm to determine game quality, woohoo!).
In the order that they popped up in my memory, and not limited to five because I'm too tired to count right now:
Pro Wrestling
Goonies II (and not because the game rewards you with a topless girl at the end)
Baseball Simulator 1.000
The Legend of Zelda
Castlevania
Double Dragon
Ikari Warriors
The Karate Kid
Amused nods go to
Back to the Future (not very good in retrospect, but at least it had a DDR mini-game)
Friday the 13th (we loved it because it looked like Jason wielded a giant toothbrush)
Many of the really good games, like DuckTales, I did not get a chance to play until much, much later on. I still haven't played that Genesis Mickey Mouse titles that people gush abou. I'll get around to that, surely.