Many years ago, I created simple tunes for most of the songs in The Lord of the Rings so I could really sing them while reading the books aloud to my son. Recently, I've begun posting videos of myself singing them on YouTube. Here's a page I've put together that collects them all (all that I've found time to do so far) in one place:
http://www.freemanng.net/hobbitsong
I hope you all enjoy them!