They Might Be Giants cover ChumbaWumba's classic (?) song "Tubthumping:"
They Might Be Giants covers Chumbawamba
I voted for "Tubthumping" to be one of the songs on the list and still think it's actually a great song to cover. As the Johns Flansburgh & Linnell state, it has enough little parts that you can experiment with each one and the simplicity of the lyrics/song structure allows you a big enough sandbox to make your own impression. Also, expectations are so low that it's hard to not do something interesting - or, at least, pleasing.
They Might Be Giants' new album, Join Us, comes out in two weeks on July 19.
(as pointed out in the comments - check out the face of Dan Telfer - the lanky, bespectacled fellow in polo shirt with brown hair behind John Linnell - from 2:36 - 2:46)