Exeter is a town in Washington County, Rhode Island, United States. Exeter extends east from the Connecticut border to the town of North Kingstown. It is bordered to the north by West Greenwich and East Greenwich, and to the south by Hopkinton, Richmond and South Kingstown. Exeter's postal code is 02822. The population was 6,045 at the 2000 census. Exeter was named for the Earl of Exeter.