Bhutan's only airport, in Paro valley, offers one of the most challenging routes on the planet for the handful of pilots certified to navigate it, but it also sets the stage for the magnificent vistas you will see along your journey. (It's a rare flight where a soundtrack of "oohs" and "ahs" don't accompany the descent.) At this writing, there is one daily flight from Bangkok on Druk Air, the national airline, by far the most direct and reliable way to enter the country. Depending on the day of the week, the flight stops en route to Bhutan in Daka, Bangladesh, or Calcutta; you can save some money by picking up Druk Air in those countries, but frequent delays due to weather could mean being waylaid in those places, too.
Beware: Druk Air now allows guests to book their airfare directly online and pay by credit card—a nice change from having to wire around $800 round-trip per person beforehand. However, do not book your ticket or arrive at the airport without a Bhutanese-government issued visa and tour operator expecting you on the other end.
Starting in 2010, the Nepalese airline Buddha Air started service to Paro from Kathmandu, but due to the small size of the aircraft and the mountainous passes, it's reportedly not always reliable.
Druk Air. www.drukair.com.bt.
Budha Air. www.buddhaair.com.