You can find free Shuttle Bus from both Suvarnabhumi (BKK) and Don Mueang (DMK).
The shuttle bus starts running from both airports at 5.00 and the last bus leave at 24.00. The bus departs every 12 or 30 minutes depending on the time of the day. The route takes approximately 50-60 minutes to another airport.
However, it might take twice that time when using shuttle bus service during the rush hour or heavy rain as it may be delayed due to traffic congestion.
AOT operate "limos" out of the Airport. They have a desk in the baggage claim area and also in arrivals. Rates to the lower Sukhumvit area start at around 1000฿ for the cheapest vehicle, and go up from there for mini-buses (for more passengers or luggage) or more luxurious options.