Thought first to start a new topic where anyone can tell about different Tolkien-based music. Well, this one is an old topic and it seems that there were even older topics like this somewhere...
Being a fan of Tolkien and Russian music here are two Russian power metal bands with Tolkien themes.
Epidemia
More Epidemia for free, legally
Epidemia - Feanor (straight link)
Arda
Few Arda songs