G-Darius on the PSX had a very strange soundtrack in my opinion. I'm not quite sure what genre I'd class the music as, but I felt it was very fitting in a lot of the situations. I also think Einhander had a very fitting soundtrack too.
Here's a video of G-Darius for those who haven't seen it before. The sound effects can drown out the music sometimes, but I think you can get a good idea of the game and its music anyway. The boss starts at about 5:00 and that has decent music too.
This video doesn't show off the strangest parts of the soundtrack, but I couldn't seem to find any decent videos which did.
It also shows how ridiculously big your ships laser beam could become (size of the screen anyone?)