I’d like to know what I said in the title. Any ideas?
Fantasy/action. The princesses and turtle people root it in the fantasy topic, whilst action is a broad enough genre to easily envelop most platformers. Combine this with both the real life SNES and Genesis being best known for platformers, and the in-game counterparts getting a bonus to action sales, and it holds up.
I thought Fantasy works best with adventure/rpg. But thanks anyway I appreciate it! 
Fantasy works well with most genres. It gets bonuses for action, adventure, RPG, and Strategy. Simulation and Casual are the only genres that don’t do fantasy well.
if only there was a sidescrolling genre
Genre Arcade/Adventure or Arcade
I don’t think that counts as a genre though.
Adventure games tend to revolve around puzzles. Mario is all about killing things via head-jumping. Either way, Mario is in the same “side-scrolling pick up power-ups and kill everything on screen” genre as Contra. I’d call it fantasy/action.
Action is a pretty broad category. That’s your shoot-'em-ups, side-scrollers, first person shooters, third person shooters, fighting games, vehicular combat, and possibly even more things I can’t think of. And that’s the idea; make the genres as broad as possible so there can be just a few of them. Most of the best-known Nintendo and Sega games from the 8 and 16 bit era fall under action.
When I think adventure games, I think stuff like Myst. Or just about any interactive fiction game (there’s one actually named Adventure). Blazing Dragons was a fun one for Playstation. Or Dreamfall: The Longest Journey for a more recent example. Combat always takes a backseat (or just isn’t included) in adventure titles.
Also, if arcade is included I think it’d work better as a platform than a genre, since arcade genre doesn’t really make sense.