I always liked "Merrily Kiss the Quaker".

My Missouri friends play something that I assume is originally from either Ireland or the UK--they call it "Soapsuds Over the Fence" but it's also called "My Love is But a Lassie Yet" or "Too Young To Marry".

Not So PC:
"Colored Aristocracy" (sometimes tamed to "Southern Aristocracy")
"Booth Shot Lincoln" (a great tune)
"Yellow Barber"
"Indian Ate A Woodchuck", although I usually call it just "Woodchuck"

Oddballs:
"Breaking Up Christmas"
"Danced All Night With A Bottle In My Hand"
"The Fiddler's Drunk and the Fun's All Over" (more commonly called Billy in the Low Ground).
"Le Lapin A Vole' Le Giraumon", or something like that, a Cajun tune whose title I think means "the Rabbit Stole the Pumpkin".