HAHAHAHA Thank you for this question!!!!
I don't have a favorite pun in English because I love all of them. My favorite puns are the ones when people get mad when I say them.
My favorite pun in Japanese is 「手荷物は手に持つ？」 it means "do you carry luggage in your hand?" but "luggage" is pronounced the same as "carry in your hand?" It's best to use this pun at the airport when you're at the checkin counter and then they will look at you and say "yes?"