Well, the times I've personally had to stop a show were obvious...once, a fire alarm ("Please remain calm" came over a loud speaker that we couldn't stop), once the lightboard dumped to complete darkness, and once I lost all power to my pit in the middle of a musical.
I got on the god mic and calmly reassured people - the fire alarm we we knew had started in another part of the building, and basically was ultimately caused from a lack of water pressure in the building (and a water main break downtown)...we were in radio contact with other parts of the building.
Another show where I was an assistant, we had to stop because of the knife/tracking system, and the SM stopped the show (god mic) and brought in the curtain while we dealt with "technical difficulties". The audience had also seen a fly get caught up flying out - they thought that was the issue....but they were in a great Christmasy mood (it was December) and the audience actually started a Christmas singalong on their own. Scrooge even came out and asked them for a request of his, they all laughed, and then proceeded to sing it.
That said, there are many, many times that we've NOT stopped the show, despite small "disasters". If safety, etc are a concern - or loud speakers you can't stop and fire alarms - then yes, the show doesn't always have to go on...
Erin