First - DON'T FREAK OUT! It's easy to think about what it is you have to be doing and where it is you should be going - when this happens. Just STOP - take a deep breath, inhale - exhale, a few times then sit down. It's true that changing your physical position can help you deal with anger or agitation better.
Second - TALK TO AN AIRLINE AGENT. These things do happen but you should talk to an airline agent to see if there is anything that can be done about it. BE SURE that you've calmed yourself down first before you talk to anyone. No one wants to help someone who is chewing him or her out. There are many stories of people who have talked to agents and have even gotten BENEFITS from being delayed because of a layover. A lot of times due to unexpected issues airlines will offer miles, free tickets and a host of other perks to passengers who had to wait. So, make sure you're not angry or confrontational and then go and talk to the airline about what's happened.
Third - DO SOMETHING. Don't just sit there letting your anger and annoyance of the situation fester. Do something. Try reading a book or catching up on the latest fashions by picking up a magazine. It's not good to just think about how late you will arrive at your destination. This is also a GREAT TIME to catch up on work! You can get through some of the things you were behind on and couldn't pick up on the flight. Or what about giving a call to that person you've been meaning to talk to for a while now but never found the time? This would be the perfect opportunity.
Fourth - LOOK AROUND. You should always be friendly, especially to those around you. For one, these people are in the same boat as you! Why not get to know some of the great people around you. You automatically have at least one thing in common because you both are stuck waiting. And, you never know whom you could meet at the airport. Maybe a famous person, your next boss, or even a new love interest!
It can be frustrating, having an unexpected layover, but it doesn't have to be a disaster and can even work out very well! It's all about what you do with that extra time you have. Also, it's important to keep in mind that everyone has been there – so, if you have an important meeting, you can be sure that the people you are meeting have been in this situation too.