Fear not the RIAA, my friends... 
We're dealing with music that falls outside of copyright law. You see, the majority of traditional music has aged to the point where, if it was copyright at one point, the protection if offers has expired. The music is free to be played, written, arranged and performed without fear of government agents in black suits knocking on your door -- so, play the music! It's meant to be performed and shared with the drunken pub-goers of the world and unwitting family members. Enjoy the music and enjoy the learning experience!
Now, we'll do our best to choose music that's public domain; however, if you should happen to realize that a tune we've posted is still under the protection of a copyright, please contact us as soon as possible and we'll get it pulled as soon as we confirm the copyright.