I was reading the thread on worst covers just now, which brought to mind good covers. I would like to submit David Bowie’s Wild is the Wind. I believe it was first sung by Johnny Mathis in the eponymous film, but there are at least two versions by Nina Simone that I admire.
Several genres figure covers, perhaps notably folk, especially Celtic tunes. Of these I particularly like Christy Moore’s Black is the colour, and Natalie Merchant’s crazy man Michael.