Heathrow Airport - connects with Totnes by train
(journey time approximately 3.5 hrs, train frequency 1 an hour).

Either go into London Paddington on the Heathrow Express, and then take a direct train to Totnes
Or, take the bus/rail connection: Airport Bus from the Central Bus Station to Reading. Train from Reading to Totnes.
Both take approximately the same time. The bus/rail link is cheaper.

Gatwick Airport - connects with Totnes by train with one change at Reading
(journey time approximately 4.5hrs, train frequency, 1 an hour)

Exeter Airport (closest airport - 1 hour away, but a minor airport)
Airport Bus to Exeter St Davids Station.
Train to Totnes (30 min journey, frequency 2 an hour)

Bristol Airport
Airport bus to Bristol Temple Meads Station (several an hour)
Train direct to Totnes (1 hr 45 min journey, frequency 1 train an hour)

Birmingham International Airport
Direct 3 hour journey to Totnes by train