Walk:After sitting in the car, on the shuttle bus and on a plane, stretching your legs is a great idea.Exercise is easy in the long concourses of an airport and if you carry your backpack it just increases the workout value. No one will look at you funny if you jog either - they will just assume you are trying to make your flight.
Plane Spot:Increase your knowledge of planes by counting the number of different aircraft models, counting the different airlines you can see, or studying how often flights take off and land. Observing airport operations can be really interesting.
Chat: Look for other travelers waiting and start a conversation. A good lead in is "where are you headed?"The conversation can be developed from there.
Window Shop: Many airports have become high-end shopping malls worth browsing.
Read: Look for newspapers or grab a good book. Most airports have quiet areas designed into them, and others just develop dead spots at various times of the day. Explore for one of the quiet corners that others rush right past and settle down for a good read.
Admire the Art: Many airports use their large-scale space to display unique, even monumental art.
Collect Stamps: If you are going to be on a layover in another country for more than a couple hours, why not head out through immigration and see the town nearby.Even if you only have a couple hours it is fun to stash your carry on and exercise that passport. It is a great way to add to your collection of countries visited.
Look for Unique Features: Check pamphlets and airport maps or ask at the info desk about unusual features in the airport. Vancouver BC has a flight simulator you can fly all over the province while you can see 4-D movies in Hong Kong. Seoul's Incheon International Airport features a golf course, while Kuala Lumpur International Airport features the world's only glass enclosed rainforest.