My favorite close call to almost being onstage was on tour in Michigan once, where I got woken up at 1am with a violently ill actor, who was so sick she couldn't even sit up in bed.  So, being the kind and generous person that I am, I actually waited until 5am to call my boss and wake him up to discuss solutions for our 10:00am school show that day.  He told me that I was going on for her.  So, I'm a techie, I don't travel with nice clothes, and the character was a russian immigrant girl from the turn of the century.  So, at 5:30am I was at Mejers, the local equivalent of a Walmart, and the only thing even open at 5:30 in the morning, trying to find SOMETHING to wear that was vaguely female/historical.  By the time I got back from shopping, it was time to wake up the cast and get them prepped for the day's fiasco.  To make a long story short, once we started brainstorming, we worked out how to re-write the script without the female romantic lead, in about an hour without any rehearsal, and I was able to later in the day thankfully return everything that I had bought, unworn!  I was never happier in my life!
-Centaura