Usually it’s when a player grabs a session and pulls it in a totally new direction.
The classic example in The Watch House was, of course, the time I was about to reveal that Natalie’s too-good-to-be-true new potential boyfriend was a villain, but Matthew’s player had him jump way further with the too-good-to-be-true part and make him magically appear as CAPTAIN RUGGED.
More recently, a planned Vampire: The Masquerade 20th Anniversary Edition session was paused for a week as Marcie the Malkavian was revealed to have diaberlised her sire - when her player had him take over her body...
And sometimes it’s when I haven’t quite figured out the rules, and oh, that monster just took over half a PC’s hit points in a single hit. But it’s been a while since that happened.