There are a few. When I was reading the Hobbit for the first time, my favorite CD was by Joy Williams, and listening to that CD (haven't done that in a while) reminds me of the Hobbit, espcially the song
Touch of Faith. I doubt many people are familiar with it, though.
I am dead serious with these next two, though they will certainly take some explaining: "The Church's One Foundation" (for any who are familiar with this hymn) and "Oh Christmas Tree," for very similar reasons. The tune of the former fits very well with the words to Boromir's riddle (Seek for the sword that was broken...), and so am reminded of such when I hear the song. The tune of the latter fits very well with the words to the Elves' song to Elbereth in "Many Meetings," though the ending doesn't fit quite right. I figured that out this morning.
A Elbereth Gilthoniel
silivren penna miriel
o menel aglar elenath!
Na-chaered plan-diriel
o galadhremmin ennorath,
Fanuilos, le linnathon
nef aear, si nef aearon!
Don't ask how I get these things. I don't know.
