Another two that come to mind are that one about the lady sailing down the Nile on the back of a crocodile, and the one that goes:
Don't go in the lions' cage tonight, mother dear, For the lions are ferocious and they bite, mother dear, And if they take a hairy fit, they will tear you all to bits, So please don't go in the lions' cage tonight, mother dear.
I've often wondered if they have been recorded by anyone. My mother used to sing them to me and swore she had learned them out of a songbook, not made them up.
Speaking of singing to children, did anyone read the recent article, I think in the NYTimes, that says children are more likely to learn to sing themselves if sung to while still babies? I've always maintained this and am pleased to see that I have been vindicated by modern science.