I've heard it (Amazing Grace) sung to the Gilligan's Island theme, as mentioned above. It is indeed quite silly but the kids love it. We did it on the guitar complete with key changes and all; it was a blast.

Now, (warning! thread creep) one of my fellow re-enactors mentioned the other night that you can sing "The Minstrel Boy" to the tune of Gilligan's Island! Horrors!!