Genesee is a town in Allegany County, New York, United States. The population was 1,693 at the 2010 census. Genesee is in the southwest corner of the county, southeast of Olean.
According to the United States Census Bureau, the town has a total area of 36.3 square miles (94.0 km), of which 36.3 square miles (93.9 km) is land and 0.039 square miles (0.1 km), or 0.13%, is water.
The south town line is the Pennsylvania (McKean County) border, and the west town line is shared with the town of Portville in Cattaraugus County.
New York State Route 417 is an important east-west highway through the town.
As of the census of 2000, there were 1,803 people, 661 households, and 493 families residing in the town. The population density was 49.7 people per square mile (19.2/km²). There were 800 housing units at an average density of 22.0 per square mile (8.5/km²). The racial makeup of the town was 99.11% White, 0.06% African American, 0.11% Native American, 0.33% from other races, and 0.39% from two or more races. Hispanic or Latino of any race were 1.22% of the population.
There were 661 households out of which 38.6% had children under the age of 18 living with them, 61.9% were married couples living together, 7.1% had a female householder with no husband present, and 25.4% were non-families. 19.7% of all households were made up of individuals and 7.7% had someone living alone who was 65 years of age or older. The average household size was 2.73 and the average family size was 3.12.
In the town, the population was spread out with 28.8% under the age of 18, 7.7% from 18 to 24, 29.6% from 25 to 44, 23.8% from 45 to 64, and 10.1% who were 65 years of age or older. The median age was 36 years. For every 100 females, there were 101.7 males. For every 100 females age 18 and over, there were 103.5 males.
The median income for a household in the town was $38,563, and the median income for a family was $44,100. Males had a median income of $31,047 versus $22,557 for females. The per capita income for the town was $16,169. About 8.9% of families and 11.8% of the population were below the poverty line, including 13.7% of those under age 18 and 5.4% of those age 65 or over.