Mohawk & Headphone Jack, for SNES, from Black Pearl.
Seriously, other than perhaps MetalStorm no game fits this label any more perfectly... except that Mohawk & Headphone Jack does some other things that make the game unbelievably, ridiculously confusing. It's easily one of the most disorienting games ever made, and that's WITH a map of the level you can scroll around!
Essentially, M&HJ is a 100% Mode 7 platformer. The levels rotate. Your character stays standing upright, in the middle of the screen, while the level rotates or spins around you. Levels are enclosed spaces -- there is a "floor" all around the edge of the level. Every surface has its own gravity that depends on its size, so that when you're on a floor and jump up and there is a platform (with a floor surface facing you -- a small round platform, for instance) at some point you'll get caught by that platform's gravity and the screen will flip around and you'll be on the platform, looking up at the floor you just jumped from (because remember, unlike a MetalStorm, here your character always stays right-side-up while the level flips around behind you...).
Oh yeah, and did I mention that you can run really, really fast? Like Sonic fast? You can. There are also very few enemies in the game (though the ones that there are can be tough to avoid because when you're running at full speed there's no way you'll see them... just use spike-ball form (you attack by turning into a spike ball, so you can do it while moving) and hope you run into them, or memorize their locations...
You complete the level by collecting 100 CDs and then finding the level exit. There are a lot of CDs so that part isn't hard... it's finding the exit that can be. Collecting special giant CDs unlocks additional music tracks. (and there is password save so you don't have to start over each time, thankfully) Oh yes, your characters are these really strange guys made of putty or something... they can squeeze through very narrow tubes (turn flat), they attack by going into spike form, some special powerups add things like wheels on the bottoms of the sprites instead of legs... oh yeah, they're naked, though since they're made of putty or something that doesn't matter much...
Seriously, without that map you can access on the pause menu the game would be IMPOSSIBLE. You just get so totally disoriented so quickly... it's a very interesting and unique game, but it's also almost unplayable in a way. Even so, it's worth the experience I think... it's just so totally weird and different that you've got to see it. It came out in 1995 and vanished immediately... finding almost any information about it online is very difficult. There is a decent video review of the game on Youtube, though. The voiceover isn't that great, but the video shows the game nicely... or rather, it shows how weird it is. It's kind of amazing a game this bizarre actually got published, in a way... they certainly showed what you can do with Mode 7, though, and the gravity effects are quite interesting.
http://www.youtube.com/watch?v=RepK4ZyAh8k