Last weekend, my wife (a teacher) took a group of 20 students and 2 other adults to Walt Disney World for a conference and some fun. On their flight back, they had a layover in DFW since our home airport is not a hub. Their flight from Orlando was delayed due to weather, but it should have been okay as the one from DFW was also delayed. They showed up to the gate as the second leg flight was boarding, and was told by the gate agents that they had bumped the entire group since they thought they were no-shows! After arguing with the agents for a while, the agents literally said "Well I don't know what you want me to do!"

My wife pointed out that other airlines deal with delayed connections by having gate agents meeting the plane and escorting them to their connection. No such help here, and the gate agents should have known what was going on.
My wife had to talk with a customer service rep (whose eyes got *real* big when we was told it was a group of high schoolers!). Initially they couldn't get a flight until the next day. Legally, my wife couldn't have the kids past that day. (Due to waivers, I think.) Not to mention no hotel or food money at that point. Then they wanted to split them up on different flights. Which also wouldn't work with only 3 adults (need at least two adults for all groups due to youth protection rules).
They finally found a flight that night, not to home, but a different airport two hours away. Myself and several other parents had to drive and pick them up, minimum 4-hour round trip (mine ended up being about 7!). Instead of getting home at 12 noon, they got home around 1 AM.
My wife was beyond pissed, frazzled, etc. and was on the verge of a breakdown through this whole experience. She sent an email to the airline (American, if you're wondering) praising the customer service rep for spending about 2 hours helping her get her group home. In the same note, she absolutely raked the gate agents over the coals for their screw-up that caused this whole ordeal. The school has since managed to get a payment for gas and time to get to the non-home airport, and I'm pretty sure they're still working on getting the entire trip refunded.