You can do this with a lot of songs. It isn't particularly funny, but I used to find myself singing "Cockies of Bungaree" to the tune of "The Wild Colonial Boy". And every time I hear the hymn title "A Mighty Fortress is our God" (I'm not familiar with the hymn itself), I find myself launching into "A mighty fortress is our God, DOO-DAH! DOO-DAH! a mighty fortress is our God, Oh, da Doo-Dah Day!" (well, there's another 10000 millenia in purgatory!)

Regarding doing "Stopping by Woods on a Snowy Evening" to "Hernando's Hideaway", I remember hearing about doing an Emily Dickinson poem (I think it was "Because I could not Wait for Death") to "The Yellow Rose of Texas".

I have heard at least one performer do "Stairway to Gilligan's Island."