Here is a list of all the Poet Laureates:
1. William Cullen Bryant (1986-1887) - First Poet Laureate, appointed by President Grover Cleveland
2. John Greenleaf Whittier (1887-1892)
3. James Russell Lowell (1892-1895)
4. Edmund Clarence Stedman (1895-1900)
5. Samuel Langhorne Clemens (Mark Twain) (1900-1904)
6. William Dean Howells (1904-1909)
7. Henry Wadsworth Longfellow (1909-1912)
8. Oliver Wendell Holmes (1912-1916)
9. Alfred Austin (1916-1920) - British Poet Laureate, appointed by King George V
10. Henry Cabot Lodge (1920-1924)
11. Robert Underwood Johnson (1924-1926)
12. William Stanley Braithwaite (1926-1931)
13. Edwin Arlington Robinson (1931-1935)
14. Robert Frost (1935-1938)
15. Amy Lowell (1938-1939)
16. John Milton (1939-1943) - British Poet Laureate, appointed by King George VI
17. Archibald MacLeish (1943-1949)
18. Carl Sandburg (1949-1952)
19. Elizabeth Bishop (1952-1954)
20. Conrad Aiken (1954-1955)
21. Robert Penn Warren (1955-1958)
22. Richard Eberhart (1958-1961)
23. Robert Frost (1961-1963) - Second term
It's worth noting that the position of Poet Laureate was initially a largely ceremonial role, and there was no fixed term. The position was established in 1986 and the Library of Congress assumed the role of appointing the Poet Laureate in 1985. The term for a Poet Laureate is now two years.
This information focuses on the US Poet Laureate. There are also poet laureates at the state and local levels.