Mother Goose began as a 1729 English translation of the name of Charles Perrault’s tale-teller in Contes de Ma Mere Loye (1697). The popularity of these tales as translated evidently led John Newbery to name his collection of songs Mother Goose's Melody about 1765. The nursery rhymes spread to North America.

http://www.library.utoronto.ca/utel/rp/authors/motherg.html

The farmer's in the dell-
the farmer's in the dell.
Hi! Ho! the derry O!
The farmer's in the dell.

Boys and girls come out to play,
The moon does shine as bright as day;
Come with a hoop, and come with a call,
Come with a good will or not at all.
Loose your supper, and loose your sleep,
Come to your playfellows in the street;
Up the ladder and down the wall.
A halfpenny loaf will serve us all.
But when the loaf is gone, what will you do?
Those who would eat must work - tis true.

Jack and Gill
Went up the hill,
To fetch a pail of water;
Jack fell down
And broke his crown
And Gill came tumbling after.

Ding dong bell,
The cat is in the well.
Who put her in?
Little Johnny Green.
What a naughty boy was that,
To drown poor Pussy cat.
Who never did any harm,
And kill’d the mice in his father's barn.

This pig went to market,
That pig staid at home;
This pig had roast meat,
That pig had none;
This pig went to the barn-door,
And cry’d week, week, for more.