The DC-area group Clam Chowder does a wonderful version of the medieval Deo Gratias Anglia to the tune of the Banana Boat Song. They sing one verse straight first --

Our King went forth to Normandy
With faith and might of chivalrie
Therefore England doth call and crie
Deo Gratias Anglia

before the tenor breaks out into Belafonte's

Deo!
De-e-e-oh!
Deo gratias Anglia

The calypso rhythms start, and it all goes downhill from there.

In Sacred Harp music, there's the concept of Common Meter -- 4/4 time with a particular line length. Anything in CM, such as Amazing Grace, can be sung to the tune of anything else in CM, such as O Little Town of Bethlehem, or House of the Rising Sun, or Yellow Rose, or many more.

LynnT