On 7 September 1775, during the American Revolution, the first prize, the supply Ship Unity, was taken by the Continental Schooner Hannah, commanded by Nicholas Broughton.
Read more about the Continental Schooner Hannah:
http://www.history.navy.mil/danfs/h2/hannah.htm --

1776 - David Bushnell attempts to destroy a British Ship of the Line, HMS Asia, in New York harbor with his submarine Turtle.
http://en.wikipedia.org/wiki/American_Turtle

1814 - USS Wasp captures HMS Avon.
http://en.wikipedia.org/wiki/USS_Wasp_(1814)