I find it interesting that this game was (is?) so widespread. For one or two or three years when I was a kid in the '60's, in Windsor, Ontario, this game was very popular among the girls at our school. They called it "Yogi", which I suspect was a name applied by the marketer of the glorified underwear waistband that was the sole piece of gear required.

I'll have to ask my sister if she remembers any of the rhymes.

There was another popular game played with a sponge ball in the toe of a nylon stocking - the girl would wail the ball against the wall behind her, over and under and between her legs (not necessarily in that order), while reciting "A sailor went to sea, sea, sea,/To see what he could see, see, see;/But all that he could see, see, see,/Was the bottom of the bright blue sea, sea, sea." Quite a feat, if you ask me. (I assume this is the same game that one or two people mentioned above somewhere).