Along the lines of "rubber balls and liquor", this gag relied on someone being excited enough by mystery to agree to saying 'Inspector Fanny' after everything you say. After securing this agreement, you say;

Who put you in jail?
Who let you out of jail?

And inevitably:
What did you do when a girl came around the street corner?

My love of this gag led to me writing "You will Inspector Fanny" on a bit of scrap paper and giving it to another kid I'd been playing the joke on, just to relive the finest moment of the joke. He passed it to the teacher, who proceeded to ask me if I knew what a fanny was.