I don't think there are any call-and-response jokes in Japanese, which is sort of an important feature of knock-knock jokes. As for jokes, which follow a particular pattern, there are simple plays on words, which everyone knows and which involve two words or phrases, which are (at least quasi-)homophones, usually at the beginning and at the end of a sentence, which when read without distinguishing the homophones are preferably some sort of tautology (e.g. ) or simply unintelligible (e.g. ). Some all-time favourites
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They are of a similar standard and similar to knock-knock jokes in that everyone gets the joke (or what's left of it) and everyone knows at least a couple of them. Also, everyone is free to make up their own.