A U.S. Navy Destroyer has captured a pirate ship 52 miles off the shore of Somalia. It is nice to know that with all the money we spend on the Navy it does occasionally do something worthwhile. This may be the first pirate apprehension in decades, although I don't have any data at my fingertips (yet).
Pirates were chased away but not boarded or fired upon, by a U.S. Navy amphibious assault ship on February 17, 2005 near Kuwait. Pirates were fired upon, but not captured by the U.S. Navy on April 23, 2002. Most attacks in recent times have been outside of U.S. Navy jurisdiction as they have occurred in the territorial waters of foreign states. Some recent background on the issue is here and here.
The last time anything resembling a piracy incident has killed a member of the U.S. military was on July 4, 1930 when "bandits" fired upon the U.S.S. Guam on the Yangtze River in China, and the last official death at the hands of pirates was on June 17, 1870 when the U.S.S. Mohican battled with Mexican pirate steamer Forward in the Teacapan River in Mexico.
An incident on April 24, 2004 in the Persian Gulf also killed Naval personnel, but is probably better classified as terrorism or part of the Iraqi insurgency than piracy.