Incredibly obscure 1991 Famicom game from Little Samson publisher Takeru and someone forgotten by time and the Internet called K2 Multi Creative Team (almost certainly the same staff behind Little Samson), that basically plays like “Make your own Mega Man”. The premise is, you've been visited in your dreams by a magical being known as the Tapir; he gives you the opportunity to build an avatar for yourself. You choose a head type, a body, weapon type, apply a name. Bingo, you have your own character.
Once you have a character, you're thrown into a nonlinear game world – sort of like Mega Man again, except after you select a level you have to walk there on your own. If you're in level A and you select level D, then before you get to level D you have to walk through an extensive transition between the two.
After you beat the first level, you'll be prompted to create another character. Then after another, another. Then more things happen. You might have to rescue some of them later, and that might have been a spoiler.
The game, as you can see, is what your college roommate would probably call “trippy”, if he weren't more inclined to call it “fruity”. As you play, you will encounter eggs reminiscent of those from Hudson's Adventure Island; crack 'em to get health refills, score-increasing thingamabobs, or – most intriguingly and importantly – power-ups. If your current weapon is (say) a shuriken, you'll find a shuriken. Collect a few shurikens, and your shuriken will go up a level. You can do this several times, until you get pretty darned powerful.
At the end of every level, you'll face a very Capcommy boss. Actually, the whole game positively sweats a Capcom vibe. It would be no surprise whatsoever, either in atmosphere or the feel of the mechanics and game engine, to learn that the game comes from the Little Nemo team. No, though. Different company. Obscure company. Not Capcom.
A decent English translation patch by Akujin is available online – which is probably the only place you'll ever run across the game anyway, so while you're out hunting for the one, you might as well get the other.
Apparently a sequel or remake was planned (though never released) for the PC-Engine; it was to have been called simply “PC Cocoron”, and has apparently been an enigma to PC Engine fans for years.
Also, I turned up this bit of fan art. Weird.