Not every multi-stop itinerary can be as smooth as a peanut butter sandwich. With airlines having uncompromising schedules and the world simply being an imperfect place, your weary butt sometimes will get caught in the middle of a long layover. It's a fact of travel life. Since airports are not always known for their scintillating entertainment, what you do can turn that shockingly long wait from excruciating to exceptional. 
Here are some suggestions on how to make the most of your itinerary hiccup:
Get some sleep: It's not an easy proposition but if you're stuck in an airport the best way to cheaply pass the time is to catch some zees. But as you know, terminal seating can be medieval at best. Fortunately for us, others have come before: here's a website specifically devoted to the practice of sleeping airport-style.
Take a city tour: if you have a half-day or more why not get out there and tour the city? It makes a great opportunity to see more of the world you didn't originally expect to see. Information booths can give you the lowdown on how to get to the city center and also what organized tours are available.
A few countries require at least a transit visa to exit the airport even for short periods of time, so check ahead if you're planning on doing some sightseeing.
Here's a quick list of airports that offer inexpensive half-day city tours that leave from the airport:
Peruse an art gallery: oftentimes airports have spaces set aside for art browsing. If you know you're going to be stuck somewhere, search the airport's website, find the map and see if yours has something going on.
Wi-Fi: If you happen to be traveling with a laptop or netbook computer, an increasing number of major airports now offer free Wi-Fi service throughout their terminal.
Here are two great airport guides showing a complete list of wi-fi information:
Domestic: http://www.travelpost.com/airport-wireless-internet.aspx
International: http://www.travelpost.com/airport-wireless-international.aspx
Shopping: International airports have a wealth of first-class shopping. While not always cheap, browsing is a sure-fire time killer.
Some of the best world airports for shopping:
Hong Kong: Skymart is a bright shining shopping jewel
Dubai: never closes!
Singapore: 160 shops
Paris: pick up one last handbag before you leave
London Heathrow: Terminal 5!
Make friends: If the airport has trapped you, inevitably there will be others trapped right along with you. Why not pass the time and talk to a stranger? Plus the friends you make may eventually become quite valuable.
Meditate: if you're new to this practice it might feel odd to do in an airport, but it's an amazing way to recharge and shoulder off the stress of the situation you're in. You can easily test its powers of rejuvenation.
Find yourself a halfway secluded spot, empty gates work well, perhaps facing a window so you don't feel exposed. Sit up straight in a chair with your feet on the floor or sit cross-legged with a straight back. Put your hands in your lap, partially close your eyes, relax your body and empty your mind. You can excavate all your wayward thoughts by concentrating on your breathing. Your mind will drift but bring it back by listening to your breaths. After 15 or 20 minutes you'll feel more relaxed than you did before you started and will be able to take a new mental approach to your layover situation.
Here's a great how-to on meditation and information about its benefits.
The main thing to remember is that while these seemingly unfortunate situations put a kink in an otherwise fluid itinerary, you can use them to your advantage and perhaps get a good experience to go along with it.
* photos by Vimages and Joe Shlabotnik