AOT (Airports of Thailand) offer an official limo service from BKK-cty-BKK:

Just contact Limousine Counter, Level 2, Baggage Claim Hall and Arrival Hall.
Limousines can also be ordered at the service counters outside the terminal on the 2nd floor and are be parked at the public transportation centre. You will be escorted to your car by an AOT staffer and they will assist with baggage.
AOT Limousine use a variety of vehicles including Toyota Camry, Nissan Teana, Mercedes E-class, BMW 7 Series, London Cab (TX II) & Isuzu MU-7. I always go for an Isuzu MU-7 suv - thay are comfy, clean and the driver is always smart & professional. Rates are roughly double taxi fares but are very very reliable and much more pleasent/spacious IME.