Here is the most amazing page of Tolkien Filk I've **ever** seen:
Tolkien Filk
Some of the songs are funny, satirical, absurd, what not. But there are enough carefully-word-smithed songs... well, just go there. Check out all the links.
Some truly amazing things have been done with "The Sound of Silence", "Fire and Rain", "In My Life", and even numerous Evanescence songs.
No, Really. Would I make that up??