I've tested this joke on several children ages three and four, and it never fails.
There were two kittens walking down the street, and one of them fell on its butt!
I developed this joke for one of my honorary nieces. She had just started to learn about joke-telling and asked me to tell her a joke. One of the keys to joke-telling is to know your audience: A three-year-old won't have the attention span for a longer joke, and subtlety and observational humor won't work either. It's got to be short and direct. She thought kittens were cute, and falling on one's butt was funny, so I figured, hey, let me combine the two.
When I told this joke, she fell on the floor in uncontrollable laughter. I had a winner.