For my part, Howard Shore's music still very much occupies the top of the charts when it comes to music from Lord of the Rings.
David Arkenstone released an album, something about music from and inspired by Middle-Earth. It's been ages since I've heard it.
Interestingly, there's a famous group no one has heard of called Within Temptation. They have not specifically tailored any of their songs to Lord of the Rings (that I know of) but if you search on YouTube for "within temptation lord of the rings" and check out some of the options that come up, I think you'll agree the music fits rather well. The group calls their genre "symphonic/gothic metal" which is a very unique category, shared perhaps only by groups such as Nightwish, Epica and Evanescence. I've heard samples of the other groups, wasn't as impressed. There's still a very limited number of songs I enjoy from their discography, but many of their songs mirror the epic tragedy and bitter struggles of Middle-Earth.
And I'm not just saying that because
I made one.
Here are some other recommendations:
http://youtube.com/watch?v=lN2PR8vuPGA
http://youtube.com/watch?v=_6iL6kkACZ8
http://youtube.com/watch?v=nn3agxH3Qyg
http://youtube.com/watch?v=w5PQOcyY4Mo
http://youtube.com/watch?v=djhmQtw70v0
http://youtube.com/watch?v=LMdMPwH38Ts