Dampier is a surname. People with the surname include:
Al Dampier (fl. 1950s-1960s), American football player
Alex Dampier (b. 1951), Canadian-British athlete and coach in ice hockey
Alfred Dampier (1843-1908), English-born actor and playwright, active in Australia
Claude Dampier (1879-1955), English actor
Erick Dampier, American basketball player
Jeffrey Dampier (1966-2005), American lottery winner and murder victim
John Dampier (1750-1826), English athlete in cricket
Lily Dampier (1859 (?) - 1915), Australian actor
Louie Dampier (b. 1944), American basketball player
Robert Dampier (1799-1874), English artist
Thomas Dampier (1748-1812), English cleric
Thomas Dampier (priest) (ca. 1700-1777), English cleric and educator
William Dampier (1651-1715), English explorer, the first person to circumnavigate the Earth three times
William Cecil Dampier (1867-1952), British scientist, agriculturist and science historian