Gunple: Gunman's Proof is a cool little SNES game. Pretty fun, and I recommend it, although sometimes gets a bit tough I remember. It has also some nice music.
For NES/Famicom, Mitsume Ga Tooru is an action platformer, and a GREAT one at that. Good music, good visuals, fun gameplay, you control a kid with a mystical third eye that shoots beams, and it has a translation right here too!
Samurai Pizza Cats is also another Famicom game with a translaton, and yet another action/platformer. You have a team of several characters you can swap anytime, with different abilities and while a bit on the easy side it's pretty fun. The translation itself is pretty cool, it even hacks in the english theme!
Splatterhouse: Wanpukku Graffiti is a parody platformer. A more "funny" version of Splatterhouse, and it's a pretty decent game with some good details.
Twinbee Rainbow Bell Adventure is one of those games that came out of Japan butchered. Is a Super Nintendo platformer (a not very conventional one), and the best way to play it is with a translated japanese version.