For once, the answer to a question in the headline is, "Well, quite possibly."
It's been 100 years since a well-documented case of penis captivus — i.e., penis-stuck-in-vagina syndrome — appeared in the medical literature. But that doesn't mean it's a total myth. The BBC's Health Check discusses the physiological mechanisms that could lead to such an unpleasant event and explains why there are lots of anecdotal stories surrounding something that's thought to be "vanishingly rare" from a medical perspective. Hint: While very, very, very few people end up needing medical treatment for penis captivus, there may be many more who get temporarily-but-disconcertingly stuck for a few seconds.