Man, did that ever work! Gnarls Barkley's version of "Gone Daddy Gone" was both funny and a little bit poignant, and the video is great.

Not as much of a stretch but still a genre-crosser--the White Stripes version of Dolly Parton's "Jolene"

I agree-- good cover, but the nod back to Gnarls from the Femmes is equally good:
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And of course the Johnny Cash covers (at Rick Rubin's behest, I believe) of Nine Inch Nails, Soundgarden, and others are great too.