Chartered in 1763 by Colonial Governor Benning Wentworth, the land was considered so inaccessible that the grant was enlarged, making Sandwich one of the largest towns in the state. It was named in honor of John Montagu, fourth Earl of Sandwich. The earl is said to be the inventor of the sandwich, requesting from his servant a thin slab of meat placed between two slices of bread, which he consumed while intent upon the gaming table.
The earliest European settlers arrived in 1767. By 1830 Sandwich had grown to a population of 2700, which is higher than the current population. At this time the town contained farms, stores, mills, churches, schools, carpenters, blacksmiths, and wheelwrights.
By the end of the 1800s much of the population had left Sandwich to live in cities to the west. Sandwich began to be an attraction for visitors, summer residents, and artists which continues to this day.
As of the census of 2000, there were 1,286 people, 564 households, and 390 families residing in the town. The population density was 14.2 people per square mile (5.5/km²). There were 965 housing units at an average density of 10.7/sq mi (4.1/km²). The racial makeup of the town was 97.82% White, 0.62% African American, 0.31% Native American, 0.31% Asian, and 0.93% from two or more races. Hispanic or Latino of any race were 0.47% of the population.
There were 564 households out of which 26.1% had children under the age of 18 living with them, 59.8% were married couples living together, 6.4% had a female householder with no husband present, and 30.7% were non-families. 26.8% of all households were made up of individuals and 13.7% had someone living alone who was 65 years of age or older. The average household size was 2.28 and the average family size was 2.72.
In the town the population was spread out with 22.0% under the age of 18, 3.3% from 18 to 24, 20.2% from 25 to 44, 30.6% from 45 to 64, and 24.0% who were 65 years of age or older. The median age was 47 years. For every 100 females there were 87.7 males. For every 100 females age 18 and over, there were 87.1 males.
The median income for a household in the town was $47,292, and the median income for a family was $55,417. Males had a median income of $35,060 versus $25,769 for females. The per capita income for the town was $23,714. About 3.5% of families and 6.1% of the population were below the poverty line, including 8.1% of those under age 18 and 5.3% of those age 65 or over.