"Jingle bells, Batman smells, Robin laid an egg. The Batmobile lost its wheel and the Joker ran away." is the version I heard as a kid in the American midwest. It's fascinating to me that this rhyme was international at a time in my life before I'd ever heard about the internet.

Edit: Oh, it's simple. This is the version broadcast on The Simpsons TV show in 1989 and I must have heard it second-hand from my fellow students who were allowed to watch the Simpsons.