I've just remembered one from my childhood - growing up in an Australian country town in the 50's. I remember it being done very rhythmically, but I don't remember there being any actions though. I don't think I've ever heard it since - don't know why I remembered it now:

Rin Tin Tin
Swallowed a pin
He went to the doctor
The doctor wasn't in.
He walked (ran?) through the door
And fell through the floor
And that was the end of
Rin Tin Tin.