"Where did you sleep last night" is one of my favorite Nirvana covers. It's an old folk song, and I've been meaning to track down this version.
There are a couple of different widely available Leadbelly recordings. On the albums, the most common recording is ~3:03.
The folk song is also known as "In The Pines" and "Black Girl". It's listed as "In The Pines" on Leadbelly's album, The Rising Sun Blues. It's listed as Black Girl (in separate recordings) on volumes 3 and 6 of his collected works. As a rule of thumb, "In The Pines" tends to be a bluegrass rendition.
Pete Seeger, who appeared recently with Springsteen at the inaugural memorial concert, also recorded the song at least twice. It appears on last year's album, A Tribute to Leadbelly, and as Black Girl on America's Favorite Ballads, Volume 1.
The song was also recorded by Leadbelly's contemporary, Bill Monroe; that's available on the classic album, Blue Moon of Kentucky.
The song was performed by a young Joan Baez, and a recording was issued on the album, Very Early Joan.
On the Seattle grunge scene, Mark Lanegan recorded the song before Cobain; it appears on Lanegan's 1990 album, The Winding Sheet.
The Wikipedia article has a long list of "Notable versions" of the song.
In 2006, a jazz band, Fredrik Lundin Overdrive, released "Belly-Up", containing arrangements of Leadbelly's most popular songs, including Black Girl.
Apparently the associated video is creepy ...
The video was underwhelming.