I remember as a kid I thought up a power-up for Mario: The Cheap-cheap suit. When Mario put it on he'd turn into a Cheap-cheap. But not the swimming kind. He'd become the kind of Cheap-cheap that jumped up from the bottom of the screen and moved in a direction. I figured the strength of your jump would determine how high you went, and then...Well, I was a kid.
But I realized a few days ago that I still really want a game where I can play as generic enemies. Like a para-troopa would be fun to play as. I could see it's wings working like the bunny-ears in Super Mario Land 2 -- keep pressing A to slow your descent. Some monsters would be near impossible to design a level around, like a thwomp or a pirahana plant, but pretty much anything that can move could be put in. It would even be interesting to play a Goomba who can't jump. I figure levels could have all sorts of secret paths depending on which character you're playing as. Maybe you could even take a team of monsters with you so that you could switch them around to get farther in a level.
I was also thinking maybe the monsters could respond to mushrooms. Like you start out as a Koopa Troopa who walks on it's legs and can't jump; you get a mushroom and turn into a Koopa-Troopa who walks on it's hind legs and can jump, and one more mushroom puts you into Para-Troopa territory. Certain characters would have a special move that you could use by pressing a button, like Hammer Bros. throwing hammers, and such. Or Boo becoming non-solid for a limited time.
You probably wouldn't be able to unlock Boo as a character until you beat the game, since that would pretty much unbalance all of the level designs.