I couldn't find a topic that would cover this subject so I decided to make one myself!
As we all know Westeros has its culture also and numerous bards wander around the continent and over the seas. We don't see Martin giving us as many verses as Tolkien for example but there's still plenty of songs that we have the lyrics to out there.
http://awoiaf.westeros.org/index.php/Category:Songs
A great list with the background of the songs.
And now renditions of these songs that I've found (mostly by fans):
The Dornishman's Wife
Joseph Campo's short bit, starts around 0.57
http://www.youtube.com/watch?v=g7-E7bc4VMc
Rains of Castamere
Version of some guy on youtube, called Douglas Harrison (i think?)
http://www.youtube.com/watch?v=t0xu7P-zzsk