Free music:

If you like listen to music for free online, I can recommend Spotify!
It's easy to use and very similar to iTunes. If you can put up with 1 or 2 adverts in between our set of songs (no worries! NOT in the middle of a song!), then just get started!

I found some interesting stuff, including the earlier mentioned Captain Future Soundtrack and David Bowie and Nat King Cole singing in Japanese!!

Unfortunately it is not easy to find exotic stuff like music by Eri Sugai (Japan's advanced answer to Enya) or old school Japanese Techno like that by Sons of Nintendo (no link available), of whom I happen to have a few genius tracks on my old dusty MD. But I guess there won't be any platform where you could find those!