I remember a version from the 90s in the Tampa Bay area, FL. It went like this:

A group of girls would sit (or stand) in a circle, their left hand under the right hand of the person to their left. The leader would start off by clapping her right hand to the right hand of the person to the her, they would do the same to the person on their left, etc. Clapping would start slow and then build speed to match the words. The person caught at the end of the rhyme would have to clap the next person's hand. If they were fast enough, the person to their left was out. If the person to their left was faster and removed their right hand in time, the last person would end up slapping their own left hand and would be out.

Down by the banks of the hanky-pank
A bullfrog leaps from bank to bank
Singin' E-I-O-U
Your momma stinks and so do you
Ping pong, ding dong
Daddy smells like King Kong
On his feet and on his toes
Your daddy wears
Pink
Pan-
ty
HOSE!

(Where "hose" was the word that would get you out.)

The person out would drop behind, the circle would close up and the whole thing would start again until there was only one person left - who was usually acknowledged as the fastest.