Besides running off into a kettle that the spigot was turned to the "open postion" at least a million times, several years ago I was brewing with a friend and we were running the wort through the chiller. He had been getting kind of bored anyway, but the session was about to wrap up and I went inside to do something and just asked him to "keep an eye on it". When I came back five minutes later he was standing there right next to the BK looking off in the distance not noticing that the (CFC) chiller tube had slipped off the valve and wort was just pouring on the ground.
Another time (much more recent), using my IC chiller and a recirc with a pump, I started the chilling process and went inside to help the wife with something, came back about 10 or 15 minutes later and noticed the wort temp was still at 180 degrees. Thought it was odd as it usually cools down to that point in a few minutes but didn;t give it much thought. Then came back another 15-20 min. later and it was STILL at 180 degrees. Now I was definitely in "what the hell?" mode. Turns out I had the chiller running, but left the burner on. Pretty amazed that it was able to hold the beer at 180 degrees for about a half an hour with the burner on and the chiller running!