Not really audiobooks, but so beautiful it's a perfect add-on when reading The Lord of the Rings.
The Tolkien Ensemble (founded in 1995) is a Danish ensemble which aims to create "the world's first complete musical interpretation of the poems and songs from The Lord of the Rings". They published four CDs from 1997 to 2005, in which all the poems and songs of The Lord of the Rings are set to music. The project was approved by both the Tolkien family and HarperCollins Publishers. Queen Margrethe II of Denmark gave permission to use her illustrations in the CD layout.
Permanent members are Caspar Reiff and Peter Hall (composition, singing and guitar), Signe Asmussen (singing), Øyvind Ougaard (accordion), Katja Nielsen (double-bass), and Morten Ryelund Sørensen (conductor and violin).
The Ensemble has toured Europe in 2007, combining their own works with soundtrack pieces from Howard Shore's soundtrack to the film trilogy as well as live narration by Christopher Lee.
They have their own website at http://www.tolkien-ensemble.net/.