Some 13,500 people voted in the poll, arranged by film subscription service Lovefilm.
The list is dominated by comedies, with Fawlty Towers and Father Ted coming in at second and third respectively. The only non-comedy shows to make the top ten are Dr Who, Sherlock and Top Gear, at fifth, sixth and tenth respectively.
All programmes voted for are featured on Lovefilm's streaming service.
Lovefilm editor Helen Cowley said: "With comedy featuring heavily in the top ten, the results reflect the very British dry sense of humour."
The top ten in full:
1. Blackadder 2. Fawlty Towers 3. Father Ted 4. Only Fools and Horses 5. Dr Who 6. Sherlock 7. Have I Got News For You 8. Red Dwarf 9. The Inbetweeners 10. Top Gear
Watch a classic clip from Blackadder Goes Forth below: