Money saving tip: To avoid rip-off taxis when you arrive at the airport, hop up to Departures and get a meter taxi from there. Should cost around 200 baht to get into central Bangkok.
If you do follow the above tip, make sure its a metered taxi and keep your wits about you. It can be risky taking non-metered taxi. It's rare, but tourists have been robbed and even attacked. I would advise female travellers to queue and take the official ones from arrivals. It will cost a bit more, but all journeys are logged by the queue officials and hence a bit safer.
The main airport is now Suvarnabhumi.
The main airport is now Suvarnabhumi. The old Don Muang trick of going upstairs to departures and catching a taxi that has just dropped off is much harder to achieve there, if not impossible. Whistle blowing, horn-blaring airport staff on scooters and in cars relentlessly chivvy the drivers as they drop off their departing fares, giving them no time to pick up a new one.