Well, they ain't exactly circulating on the schoolyards, but for sheer stupid and nasty, it's hard to beat Andrew "Dice" Clay with immortals like:

Jack be nimble
Jack be quick
Jack burnt off
His fuckin' dick.

Others from his "act" are HERE

The only one of his that I know for a fact WAS making the schoolyard rounds at least 40 years ago is a bit different than listed there. I remember it quite well:

Old Mother Hubbard
Went to the cupboard
To fetch her poor dog a bone.
But when she bent over,
Rover came over,
And he had a bone of his own.

Spaw