If you know you're going to be stuck in an airport for an extended period of time with a group, you can create a scavenger hunt. Make a list of things that could commonly be found in an airport. For example, maps, pilots, colored luggage and families with matching shirts make good scavenger hunt items. Have everyone pair or team up and try to take photos with as many of the listed items as possible before your flight boards.
When confronted with an unexpected delay, a simple game of Eye Spy can help pass the time. You need at least two people to play. One person looks around his immediate area and selects an object, after which he says, "I spy something..." and tells the other players the color of the object. If it's multi-colored, tell your fellow players all the colors; solid color objects, however, tend to work best for this game. Once another player has guessed the object correctly, it's then her turn to look around and choose the next.
Make your experience in the airport an educational time for your family. In most airports, there's a large board that displays all incoming and outgoing flights. While some arrival/departure boards display the state or country of the destination city, others may only list the airport or city name. Small airports may only have flights to local cities, but international airports offer flights to destinations all over the world. Try to guess in which state or country each city is located by looking at the destination cities. Ask the most knowledgeable group member for the answer or purchase a map from an airport shop. If the arrival/departure board gives away the state or country of the destinations, then a variation of this game could be played with a blank map or a list of airports to which your airlines flies.
Hide and seek is a fun game to play with friends. Airports, however, can prove dangerous places to be alone. Instead of having someone in your group hide, make the game about looking for individuals naturally scattered around the airport. One person can go through the airport and photograph employees or people waiting for flights. The other players must pair up and search for certain people among the crowds. Make sure you ask for permission before photographing anyone.