Somebody asked where the Lone Ranger takes his garbage. Along those lines, my officemate shared this one with me:

What happens when the Pink Panther steps on an insect?
Dead ant dead ant, dead ant, dead ant dead ant dead ant...

Not strange that I remember most of the ones that Alice Cascorbi gave, since I was a kid in Cleveland around the same time (maybe slightly earlier). It's more remarkable that I knew the same "Colonel Bogey" parody as Alan from Australia.

There was actually a commercial recording of the "Shaving Cream" song.

Maybe someone can fill in this cheerful one:
Jingle bells, Batman smells, Robin laid an egg,
Commissioner Gordon killed himself and ? broke his leg.