Cooperstown is perhaps best known has the home of the National Baseball Hall of Fame. Folklore tells that Abner Doubleday invented baseball in Cooperstown in 1839.

According to the United States Census Bureau, the village has a total area of 4.1 km² (1.6 mi²). 4.0 km² (1.5 mi²) of it is land and 0.1 km² (0.04 mi²) of it is water. The total area is 2.53% water.

There are 906 households out of which 23.2% have children under the age of 18 living with them, 41.9% are married couples living together, 8.7% have a female householder with no husband present, and 47.1% are non-families. 41.4% of all households are made up of individuals and 19.2% have someone living alone who is 65 years of age or older. The average household size is 2.05 and the average family size is 2.83.

In the village the population is spread out with 20.2% under the age of 18, 5.4% from 18 to 24, 24.7% from 25 to 44, 22.8% from 45 to 64, and 26.9% who are 65 years of age or older. The median age is 45 years. For every 100 females there are 81.4 males. For every 100 females age 18 and over, there are 76.8 males.

The median income for a household in the village is $36,992, and the median income for a family is $50,250. Males have a median income of $39,625 versus $20,595 for females. The per capita income for the village is $26,799. 10.2% of the population and 5.0% of families are below the poverty line. Out of the total people living in poverty, 7.5% are under the age of 18 and 5.4% are 65 or older.