Captain Krankor, the head grammarian for the Klingon Language Institute has written a number of Klingon songs. You can see a group of us at this years qep'a' singing his most famous piece, taHjaj wo' (May the Empire endure) on youtube at
http://www.youtube.com/watch?v=MnvAGY1t9es. The first couple of seconds of the song are missing though

This song is about 16-20 years old. It was orginally written for the first Klingon Language Camp in Red Lake Falls MN.
You can get the lyrics to taHjaj wo', as well as some of Krankor's other songs and some songs from other composers, at
http://klingonska.org/songs/