Richard Wigginton Thompson (8 June 1809 – 9 February 1900) was an American politician.

Thompson was born in Culpepper County, Virginia . He left Virginia in 1831 and lived briefly in Louisville, Kentucky before finally settling in Lawrence County, Indiana. There, he taught school, kept a store, and studied law at night. Admitted to the Bar in 1834, he practiced law in Bedford, Indiana, and served four terms in the Indiana Legislature from 1834 to 1838. He served as President Pro Tempore of the Indiana Senate for a short time and briefly held the office of Acting Lieutenant Governor. In the Presidential Election of 1840, he zealously advocated the election of William Henry Harrison. Thompson then represented Indiana in the United States Congress, serving in the United States House of Representatives from 1841 to 1843 and again from 1847 to 1849.

Following the American Civil War, Thompson served as judge of the 18th Circuit Court of the state of Indiana from 1867 to 1869. In 1877, President of the United States Rutherford B. Hayes appointed him Secretary of the Navy; and he held that office until 1881.

Retiring to Indiana, Richard W. Thompson lived out the remainder of his days in his adopted state. He died in 1900 at Terre Haute, Indiana.

The United States Navy destroyer USS Thompson (DD-305) was named in his honor.