"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.
We were singing this before the The Simpsons, so I wonder if it was the show that made it international or it already was that way.
I recall being 6 years old and singing the "Wonder Woman lost her bosoms" variant at primary school in New Zealand. This was 1982 so definitely sung internationally prior to The Simpsons.
Same. I was singing this in the very early 80's, if not late 70's.
[dead]