When I was growing up, we all jump-roped to "Down by the river, where the green grass grows." My grandma taught me "1-2-3 O'Leary," so I always bounced a ball with that.

I was a counselor at a camp about three years ago, and the campers (good-natured high school students) played a surprising amount of games during break time. Not surprisingly, they weren't all innocent little rhymes. For example, Little Sally Walker has been reincarnated! She's now a circle game, with the chant:

"Little Sally Walker,/walking down the street.
She didn't know what to do, so/she jumped in front of me and said:
'Hey, girl, shake that thing,/shake that thing like it ain't no thing.
Come on, girl, shake that thing,/shake that thing like it ain't no thing."

And another favorite circle game:

"Here we go, ridin' that pony, riding around on that big fat pony.
Here we go, ridin' that pony, this is how we do it:
Front to front to front, oh, baby
Back to back to back, oh, baby
Side to side to side, oh, baby
This is how we do it"

Of course, both games were stopped more than once when campers became too...involved!

We also did the fairly innocuous "Wisconsin Milk" song, and a ton of other call-and-responses that don't quite qualify as street games.