Does anyone know the stories behind any nursery rhymes?

I was told once the story behind the lullaby "rock-a-by baby", with the last line adjusted slightly:

"...when the bough breaks, the cradle will fall, and down will come baby kingdom and all..."

(talking about Edward III, I think, when his mother whisked him away out of danger).

Anyone know any more? For instance:

Hickory, dickory, dock
The woman who lived in the shoe
Sing a song of sixpence
Old King Cole
Old Mother Hubbard
Rub-a-dub-dub

Here an essay that has some information of interest to your topic:
The History of Nursery Rhymes & Mother Goose

That was interesting, thanks!