American folk song, in the public domain.

Oh, I had a horse and his name was Bill
And when he ran he couldn't stand still
He ran away one day
And also I ran with him

He ran so fast he could not stop
He ran into a barber shop
Fell exhaustionized - with his eye teeth -
In the barber's left shoulder

This nonsense song from the American folk tradition is a regular part of many children's musician's repertoire, thanks in large part to Carl Sandburg's early 20th century recordings of it (included on Flat Rock Ballads, Songs of America, New Songs from the American Songbag, and Carl Sandburg Sings Americana).

The tune is easy to sing and play (you sing it to the tune of the verses to "Dixie"), and kids find the imagery delightful, if slightly naughty (I remember learning the song in Catholic school at the age of 7, and found the reference to breaking the ten commandments quite titillating).

I had a gal and her name was Daisy
And when she sang the cat went crazy
With deliriums - St. Vituses -
And all kinds of cataleptics

One day she sang a song about
A man who turned himself inside out
And jumped into the river
He was so very sleepy

I'm going out in the woods next year
And shoot for beer and not for deer
Well I am, well I ain't
I'm a great sharpshootress

At shooting birds I am a beaut
There is no bird I cannot shoot
In the eye, in the ear, in the teeth
And in the fingers

I went up in a balloon so big
The people on earth looked like a pig
Like a mouse, like a caddydid
Like flyses and like fleases

The balloon had turned up with its bottom side high
Fell on the wife of a country squire
She made a noise like a doghound, like a steam whistle
And like dynamite

In Frisco Bay there lives a whale
And she eats porkchops by the bale
By the hatbox, by the pillbox, by the hogshead,
by the schooner

Her name is Lena, she is a peach
But don't leave food within her reach
Or babies, or nursemaids, or chocolate ice cream sodas

She loves to laugh and when she smiles
You just see teeth for miles and miles
And tonsils, and spareribs,
and things too fierce to mention

She knows no games so when she plays
She rolls her eyes for days and days
She vibrates, she yodels,
and breaks the ten commandments

What, could you do in a case like that
What can you do but stamp on your hat
Or on your mother, on your toothbrush
And on everything that's helpless

In the folk tradition, of course, there are other verses. If memory serves, I heard this one from Joe Wise:

There's bread and cheese upon the shelf
If you want any more you've got to sing it yourself
Sing it in a high key, or a low key,
or any key that suits you.