I've had to stop shows on several different occasions.
Once, a pre-teen actress passed out and fell from an 8' platform, just seconds from the final cues. She broke both of her jaws, which of course necessitated calling an ambulance and her parents. I immediately called for God Mic and said "Ladies and gentlemen, we now pause for a brief unscheduled intermission" before I tore out of the booth to attend to her. (As a side note, one of my Artistic Directors was actually running lights that night, but wouldn't address the audience, he left it up to me to figure out what to say!)
Then there was the time when a stage tech missed his spike and the gigantic turntable missed it's pivot and wedged itself against the proscenuim. This would be Opening Night of the biggest contract that I've ever worked under! Once again, "Ladies and Gentlemen, we will now pause for a brief, unscheduled, intermission!" This time, since it was opening night, everyone who built it was in the audience, and throughout the house (astonishingly like a pack of Whack-A-Moles) techies began to pop out of their seats and wander backstage. There was a little hemming-and-hawing before we reset and got going again. (This story gets a lot more detailed and funnier when I tell it in person

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Most recently, in the first act of the last show I SM'ed, power went out throughout downtown. I ran over to the tech booth (where the window slides open), and announced "Ladies and Gentlemen, we obviously have had a power outage. Please remain seated as we try to determine the extent of the problem. Crew, please escort the actors offstage with flashlights." I then went out to the lobby to check with House Management, who had already called Com Ed, and saw that the lights were out to the entire area. I then went back in and announced the postponement of the show, and had the ushers begin escorting the audience out with flashlights. We ended up cancelling that performance, and the lights came back on an hour after we cancelled the second show of our twinight doubleheader.

Stopping a show is not a fun thing, but like any other crisis, it can be handled well, or panic can ensue. The trick is to keep a level head, as is the key to Stage Management!