I believe there may be some argument for "Hangman" as being a candidate for the title. Variants of it have been documented throughout Europe, dating back many centuries.

I cannot attest to the current popularity of another song I know, but it seems to go back quite a way (forgive any spelling errors):

Flevit Lepus

Flevit lepus parvalus
Clamens altis vocibus
Quid fecci hominibus
Quod me secunter canibus? (repeat X2)

Roughly translated:

The Little Rabbit

The poor little rabbit
Exclaims in a loud voice
Why makes men
Always chase me with dogs? (or sticks, depending upon translator)