I love old folk songs, this tune is actually kind of a mashup of two songs, it's the lyrics from Matty Grove (which dates back to the 17th century!) and the melody of Shady Grove, a traditional Appalachian folk song.
Since I'm already geeking out, my favourite version of Matty Groves is Doc Watson's cover, and my favourite version of Shady Grove is Jesse Stewart's "Shitty Groove".