What should have been about 9 hours turned into 26 hours. We arrived at McCarran Airport at 3 AM for a 6 AM flight. We checked in on computer And awaited our names to be called to have the luggage checked. At 5 am We complained and found out that we had no luggage to check because we checked in to early. We had to check in again. Got the luggage checked & ran to the plane. 5 minutes before scheduled takeoff. We flew on American Airlines to Dallas /Fort Worth For a transfer to Philadelphia. We were plenty early for this flight. about 30 minutes before scheduled takeoff they announced a delay. Mechanics were working on the lavoratory. several announcements & 2.5 hours later the flight was cancelled. We now had to await a rescheduling. Some people were flown to Chicago, some to Miami, Some to Newark all with connecting flights to Phila. We were chosen for Washington DC On American with a connecting on United to Phila. After arriving in Washington we were told that the flight to Phila. was overbooked & we were placed on standby. The plane took off without us. They booked us on a commuter plane for 8:18am the next morning. We were then sent to a United booth to get a free hotel for ther night. United said it was an American problem & sent us there. American was closed. travelled back to United & had a drag out fight with them. After a while a superviser got in on it & listened to our story. She approved the stay. They gave us a $60 taxi voucher for a ride to a free room at a Hampton Inn in Virginia., food vouchers totaling $30.( good at Airport) & 2 free tickets on a future flight. We arrived at Hampton Inn at midnight. Left a 5 AM wake call. Next morning they could not locate the shuttle bus driver to bus us back to Airport,so they paid for a taxi fare back to Airport. We got to airport in plenty of time to use our food vouchers for breakfast. Plane was delayed 30 minutes awaiting for fuel. 11 am & back in Philadelphia we began our luggage hunt. United did not have it. American did not have it. Well we eventually got it. American Airlines , you lost 2 customers.