The Town of Rumney contains several smaller villages. Rumney Village, the town's central settlement, lies just north of the Baker River. Directly to the south, across the Baker River and adjacent to Route 25, is the village of Rumney Depot. The village of Stinson Lake, comprising development around the lake and at the foot of adjacent Stinson Mountain, is in the northern corner of the town, and West Rumney is located along Route 25 near the town's western border.
Rumney is home to the "Polar Caves" which are well known for their geological views and glowing rock formations. It is located along Route 25 near the town's eastern border.
There were 569 households out of which 29.9% had children under the age of 18 living with them, 57.5% were married couples living together, 6.3% had a female householder with no husband present, and 30.8% were non-families. 23.2% of all households were made up of individuals and 8.8% had someone living alone who was 65 years of age or older. The average household size was 2.55 and the average family size was 3.00.
In the town the population was spread out with 25.4% under the age of 18, 5.5% from 18 to 24, 25.9% from 25 to 44, 27.0% from 45 to 64, and 16.1% who were 65 years of age or older. The median age was 41 years. For every 100 females there were 102.7 males. For every 100 females age 18 and over, there were 102.2 males.
The median income for a household in the town was $38,125, and the median income for a family was $42,895. Males had a median income of $26,594 versus $21,705 for females. The per capita income for the town was $17,169. About 4.9% of families and 9.5% of the population were below the poverty line, including 15.0% of those under age 18 and 6.7% of those age 65 or over.