When they mess up, they do so badly, and with utter contempt for the passengers.
My wife and I had round trip business class tickets from Frankfurt to Dallas, for which we had paid a nice hefty price. The flight TO Dallas on April 10th, was fine.
On the way back, on May 15th, we got to the check-in counter about two hours before flight time. They kept us hanging there for about 90 minutes, saying "they had to check something, we will be right with you," and then told us we were there too late to check in, and since it was our fault that we were late, they would not pay for a hotel or offer any assistance. They had obviously overbooked the flight, and were under instructions not to offer any compensation. They booked us for the next day, claiming ALL connections to Europe for the 15th were fully booked up (sure they were), and then said get lost, we have other customers to serve. I missed an important appointment for the following Monday in Zürich that could not be rescheduled. The shocking "F*** You" attitude of American shocked even an experienced traveler like me. When I complained afterward, and said they should at least reimburse me for the hotel cost ($129, and we had paid $6000 for the air tickets), they said get lost. Needless to say, we will NEVER take American transatlantic again, and avoid them like the plague domestically as well.