Exeter is a town in Penobscot County, Maine, United States.

Dr. John Blaisdell acted as agent for early proprietors.

There were 491 housing units at an average density of 12.7 per square mile (4.9/km2).

The racial makeup of the town was 97.9% White, 0.5% Native American, 0.3% Asian, and 1.3% from two or more races.

20.3% of all households were made up of individuals, and 6.9% had someone living alone who was 65 years of age or older.

There were 452 housing units at an average density of 11.8 per square mile (4.6/km2).

The racial makeup of the town was 99.00% White, 0.80% Native American, and 0.20% from two or more races.

18.3% of all households were made up of individuals, and 6.9% had someone living alone who was 65 years of age or older.