No one likes a packed airplane, but you might if you got a free ticket out of the deal.
Airlines often overbook flights, meaning that the airline has sold more tickets than there are seats available on the flight. There are a couple of reasons that this happens. The main one is that airlines want to make sure that their planes are always full. To make sure of this they sell more tickets than there are seats to compensate for traveler who don't show up for their flight.
As a result people are bumped from the flight. Airlines are legally required to compensate travelers for the inconvenience, usually several hundred dollars, or a free ticket.
Recently my wife and I flew to Idaho from Oregon when an overbooking occurred. The woman at the Horizon counter announced that whoever was willing to give up their seat on the flight would get a $300 voucher with the airline for later use.
Being on a time constraint, we didn't go for it, however it is a deal I will listen for when I am in an airport in the future. Without fail several people popped up to go and get themselves a deal.
If a person had some extra time, and didn't need to get where they were going in a hurry you could get a free flight out of the deal. Compensation varies greatly from airline to airline. Before you volunteer to be bumped from a flight make sure to get the details of what they are offering you to make sure that your delay is worth your while. Typically the longer the flight is the greater the compensation, so if you're on an international flight you could potentially get much larger compensation than they offered for our relatively short flight.
You might also be entitled to a hotel voucher if you are delayed over night. Just ask, it can't hurt. The airline is in the awkward position, so try to get all you can out of the situation.
The next time you're waiting around in the terminal for your flight to board keep your ears open. You might just be able to get yourself another flight for free, and who doesn't like free things.