The soundtrack of Revenge of Shinobi was created by Yuzo Koshiro, a famous composer of video game and chiptune music. I only discovered this years after playing the game, but during the release of the game he must have been quite famous already: the title screen explicitly mentions him.
The soundtrack has an official release that features the uncompressed music before it was made into the Megadrive version. I like the Megadrive version better as the compression adds some punch and darkness to the drumbeats.
You can find the SEGA Megadrive rip here: KHInsider.com.
If you're going to play this game, be prepared to use save states or memorize every level..it's hard as nails (but worth it).
The OST contains some wonderfully funky tracks, grooving and jazzy. Other tracks like the boss music are menacing and fast-paced.
The highlight of this OST for me are the drums, which have a characteristic muffled sound. Then there are some beautiful melodies like in 'China Town' and the balled 'My Lover'.
The track 'China Town' has a certain melancholy to it, and the level adds to that feeling: you wander around a non-descript city, the lights of skyscrapers in the distance, a single stoplight in the street.