A friend of mine plays mostly blues, and also does some lovely flemenco style guitar. One night someone asked him to do some flemenco, but he really wanted to do House of the Rising Sun instead - so he sang it with flemenco guitar accompaniment. I thought it was brilliant!

Also on the House of Rising Sun theme - my daughter also likes to play with songs & change them around a bit - and she had worked up a good variation. Unfortunately as soon as she started singing it (despite a very specific introduction) another friend of ours started singing along to the more usual tune. I had to ask him to shush - for which he alleges never to have forgiven me (though if he'd listened to the introduction he'd have known...........).

Picking up on the Kate Rusby version of Wild Goose (mentioned above by keith) - I fell in love with the song from her version, but then opt to sing it my way by changing some of the words a bit & doing it as a fast blues/shanty. It seems to be happy both ways.