I LOVE House of the Rising Sun! I did it at a talent show once years ago. You can also sing the words to Amazing Grace to that tune. It's very moving.
1) I haven't scanned through all the posts, but I'm surprised I haven't seen "Amazing Grace" mentioned yet.
2) There's a group of Mensans who have made a running comedy bit out of singing "Amazing Grace" to many different tunes at Mensa functions, including "Ghost Riders in the Sky," "Macarena," and the "Gilligan's Island" theme.