Tristan da Cunha
Tristan da Cunha is officially the most remote inhabited archipelago in the world, sitting 1,750 miles from the nearest land in South Africa. The main island of Tristan da Cunha is 7 miles across and a little under 38 square miles in all and has a permanent population of less than 300. The islands were discovered by Portuguese explorer Tristão da Cunha in 1506. The island wouldn't get its first resident until American Jonathan Lambert showed up in 1810. He declared the islands his own but died in a boating accident only two years after establishing his empire. Eventually, the island came under the control of the United Kingdom where it remains today, a British Overseas Territory with Saint Helena and Ascension Island.
Most citizens live in the settlement of Edinburgh of the Seven Seas, where residents make a living farming or working for the local government. The island makes a fair amount of income from the sale of coins and stamps from this unique British postal code. Health care on the island is free, but serious injury could necessitate flagging down a passing fishing vessel to ask for a 1,750-mile ride to Cape Town, South Africa.