BKK (Suvarnabhumi Bangkok International Airport), all three major mobile service providers: AIS/One-2-Call, DTAC/Happy and TrueMove/H all have staffed store-fronts on level 2/Arrivals, just outside Customs. I've personally seen these shops open as early as 6:00 AM and as late as 12 midnight.

But if the line to get a SIM is long, and I've seen dozens of people queued up there, just go to any convenience store or mobile phone shop - of which there are several million in any 2 block radius - to purchase a SIM and top-it up. Any DTAC/Happy SIM (49 baht, usually comes with 50 baht of calling time) can be used to layer on a weekly internet plan (199 baht) and 100 minutes (100 baht) for essentially the same promotion.