Human scavenger hunt
Go and talk to the people around you. Try to find the most interesting or inspiring life stories. The elderly man in the corner, maybe he used to be a famous ballerina and lived a glittery life in the 1960s London. Or maybe the 11-year old in the corner just launched what will become a world changing movement for peace. One cannot know til´ one asks.
Play hide and seek all over the airport or hide little treats and draw a map for you fellow travelers so they can find it. Or why not put all the luggage together and build a fort? Kids are sure to be up for this and their parents will probably be thankful for some distraction.
It doesn´t have to be in a romantic sense of course, just a way for people to start talking. Scoot out a good location and give people a time limit (5 minutes or so) before they need to move on. To make it more interesting, give them a specific topic to discuss. Hopefully you will all have heaps of new friends before the flight departures.
Go prank people in the airport and film it. How about flirting using only lyrics from One Direction songs or approaching a stranger exiting the arrivals hall telling them something random, like they´re late and you need the suitcase now to close the deal. Remember to ask for their permission before you post it on YouTube!
Go on a date
Why not take this moment to ask that beautiful person you have been eyeing since you got there if he/she would be interested in a coffee date at one of the airport cafés? You never know, true love has been found in weirder places. If it doesn´t work out, well, you probably won´t have to see each other again.
Create a flash mob
Hundreds or even thousands of people of every age from all over the world gathered in one place with nothing to do. Is there really a better place to try and start a flash mob than at an airport? Teach them some simple steps that everyone can do and voila, you just became international superstar.