What type of music is this, and where can I hear more of it?

You can purchase the soundtrack. The music was composed by Howard Shore and played by the London Symphony Orchestra. Here is more information from Wikipedia.

Here is the track listing for the first film, An Unexpected Journey, with sound samples: http://www.amazon.com/The-Hobbit-Unexpected-Original-Soundtrack/dp/B009O07NBQ
Disc 2, Track 7 “Under Hill” is the segment from the Goblin caves, I believe.

@hearkat don’t think this is it.

I’m most interested in learning about the type of singing, the chant-like dramatic voices that accompany the music…

“Ominous Latin chant” like a dramatic Gregorian chant

http://www.youtube.com/watch?v=GD3VsesSBsw&list=PLC8F786DD0F303C2F&index=3

@ARE_you_kidding_me yessssssssssssss!!!!

http://www.youtube.com/watch?v=-zzsRlnvmlY

Well, the sound sample is a short clip. I was just going by the chronology of the movie, that sequentially that track should represent what plays during the scene in the goblin caves.

@ARE_you_kidding_me O Fortuna was the first thing to pop into head for me as well.

One of the only good things to come out of the Star Wars Prequels

@JonnyCeltics There are a lot of good examples on this page.

Thanks @uberbatman! John Williams FTW!