The Italian R.E.M. fanzine, BAZAR, has a list of what I believe to be various bootlegs, rare tracks, and duets done by R.E.M. and/or Michael Stipe (lead singer) with other artists.

I've tracked down a couple of them so far, including Michael Stipe and Radiohead performing R.E.M.'s E-Bow The Letter from New Adventures in Hi Fi.