Thompson was asked by Rolling Stone to present his list of the best songs of the millenium- which he very graciously did, including many medieval songs (in Latin!) in addition to a very few songs from this century. Rolling Stone didn't publish his list, so Richard put the songs together into a revue, which he performs every now and then (always solo acoustic!) his version of "Oops, I Did It Again" is included in the recording he made of those songs. Its pretty incredible, and shows you what even a piece of trashy pop music can be in the hands of a master musician. His guitar accompaniment is one of the most bizarre and rewarding short musical pieces I've heard in a long time! NPR had a streaming audio version of "Oops.." on their website, and its probably still available. Also included in the NPR set, by the way, is a wonderful version of "The Blackleg Miner", which has been one of my favorite labor songs for many, many years.
I was also thinking about Luka Bloom, who isn't "straight" folk, but who plays acoustic folk/pop- he's done covers of songs like "I Need Love" by LL Cool J, and "When Doves Cry" by Prince. He's also been known to cover U2, The Waterboys, and (!) Radiohead.
Back to the surprising folk music from unexpected sources- the Waterboys album "Room To Roam" has some wonderful stuff on it. Most of the lyrics are by Mike Scott, but the music is beautifully steeped in the folk music of Scotland and Ireland.