I travel quite a bit with my job and I've missed my fair share of flights but I've never reacted like this woman...
My top 3 list of bad airport/airline experiences:
1. Sao Paulo to New York (American Airlines). Missed my connection due to delays flying from a conference in another Brazilian city. Rushing between gates was not helped by the fact that I was carting a 1m long fiberglass fish that I had bought at a flea market. Was eventually placed on the next flight to New York and was fortunate enough to score two seats...one for me and one for the fish.
2. Singapore to Sydney (Qantas). This was caused by a delay in Finland, resulting in a missed connection. The flight from Helsinki was the scariest flying experience I've ever had....the plane accelerated on the runway then braked suddenly. My immediate thought was that we were going to hit another plane but apparently it was due to a warning light in the cockpit. The plane was fine but we had to wait two hours for the engineers which meant I missed my flight from Singapore to Sydney.
3. LA to Sydney (Qantas). The flight crew were involved in a car accident on the way to the airport. They weren't allowed to fly and so we had to wait for replacement crew.