Thus, if you're a Tolkien nerd, elves should sing, regardless of how modern teenage boys (or arrested man-children) may rank it on the dorkiness scale.
Orcs and goblins, being corrupted elves (at least during part of Tolkien's theorizing, he waffled on this issue a bit), also sing. They probably don't actually sing "Where there's a whip, there's a way," but they do sing nasty little made-up rhymes, and in The Hobbit, when the dwarves are captured and dragged down, down to Goblin Town, the fact that the goblins are singing "Whip crack, bones snap!" all the way is a major addition to the creep factor of the scene.
All of which leads me to be reasonably chuffed by my discovery of this, which apparently appears in the "Director's Cut" DVD version, even though it was sadly omitted from the theatrical release:
Now, this is not without issues, not the least of which is "Where is the freakin' orchestra?" This would be ten times better if it was an a capella chant, with the Goblin King's cronies providing the "music" by chanting and effectively beat-boxing their way through it. Instead what we've got is a parody of a broadway musical number, and while that's actually kinda cool in its own way (goblins being a mockery, and all), it doesn't make a lick of sense in context.
Still, I'm amused, and if they'd included in the theatrical release I would have thought a lot more highly of the film.
EDIT: I see on re-watching that there is a goblin orchestra, shown early on. I missed it in the sea of taupe.