Chester Arthur assumed the Presidency after James Garfield was assassinated in 1881.  Though he was assumed to be a party stooge, his term saw the attempted reformation of the political favor system.  Birthplace: Fairfield.
Calvin Coolidge became president after the death of Warren G. Harding, and his first task was to clean up the problems Harding had left behind.  His term was based on a pro-business fiscally strong stance, though the Depression occurred the year after he left office.  Birthplace: Plymouth. 
George Dewey was a famous naval captain who destroyed the Spanish fleet at Manila in the Philippines during the Spanish-American War.   Birthplace: Montpelier.
Stephen Douglas was one-half of the noted Lincoln-Douglas Debates.  He believed that states should decide for themselves whether they wanted to establish or abolish slavery, and his sponsorship of what was called the Kansas-Nebraska Act led to the fiery debates.  Birthplace: Brandon.