Here's the best versions I could find of "The Misty Mountains" and other Tolkien songs.
A pretty good A Capella version; I understand why they didn't use the whole song in the movie, but it's still a shame we didn't hear the whole thing.
An Ocarina version
A deeper bass version; took a bit of getting used to, but I like it overall.
What they might have done if they extended the movie version.
A follow-up to the previous one, with verses from The Fellowship of the Ring (the book, not the movie).
Another version of Song of the Lonely Mountain, the number sung by Neil Finn in the closing credits of The Hobbit: An Unexpected Journey, not written by Tolkien, but based on "Misty Mountains".
The "Song of Durin" from the book Fellowship of the Ring,
All the verses of "Misty Mountain", done by a woman