The one I remember best was a clapping sort-of patty cake rhyme with two completely unrelated verses. But we always did both, the second one right after the first.

The clapping was done sitting across from your best friend.

The clapping steps were:

1) Clap your shoulders with your arms crossed.
2) Clap the top of your thighs
3) Clap your hands together
4) Clap your right hand across to your friends right hand.
5) Clap your hands together.
6) Clap your left hand across to your friends left hand.
7) Clap your hands together.
8) Clap both your right to your friends left and your left to her right together.

Repeat over and over. One clap per syllable to the following verses:

My mother told me if I was goody
That she would buy me a rubber dolly
My auntie told her I kissed a soldier
Now she won’t buy me a rubber dolly.

Three Six Nine
The goose drank wine
The monkey spit tobacco on the street car line
The line broke
The monkey got choked
And they all went to heaven in a little rowboat.
Clap-clap.