http://www.coversproject.com/ is a great site for something like this.
I was suprised to learn the Pogues "Cotton Fields" is a very loose cover of a Leadbelly song by the same name. More like a bit of sampling actually.
I got into the Pogues because I heard "Whiskey in the Jar" by Metellica was originally by some Irish band. A search turned up a version the Pogues did, but the song was originally done by a band called the Dubliners.
EDIT: haha, I was typing this before the post above came up. I'm sure the "original" original dates further back. I think the Dubliners were the first to record it though.