My two worst ones were due to dodgy cables made by someone at Marshall Music CT.
1) Playing at the Waterfront for a competition (we had no idea it was a competition) my brand-new 8m Mogami/Amphenol lead (1 day old) broke. It took my 3-4 songs to find out it was the cable and I had to entirely bypass my pedal board.
2) Playing on a TV film set for a one-shot recording of our set for a Kyknet TV show. 4 songs in and my 3m Mogami/Amphenol cable made by the same guy breaks and again, I have to bypass my pedal board.
As a result, I now own two (lesser quality) seriously durable woven DiMarzio 6m cables. Will get some better quality, solid cables when I get more cash flow. Will repair the Mogami's myself when I get time.
One thing that's happened often is power/PA's cutting out, but since 4/5ths of my one band (Nomadic Orchestra) are acoustic anyways, we're quite comfortable with power going out. In fact, it probably adds to our show.
Last time it happened, I told all the brass players to jump on the bass bins and play an extended intro to one of our songs (which starts with an already long horn intro). We did the first bit of the song acoustic and the horns continued through the first few sections, drums and guitar waiting for the power to come on. Once it came on we waited for a break so we could come in full-force again in a musical way. Worked great!