I heard a story from another marine who was with a MEU a few years ago about pirates off of somalia, I'm not sure if its true, but still entertaining. Supposedly these pirates were within range of a navy ship and one of the pirates freaked out and fired at the ship with some sort of small arms. The navy gunners requested permission to fire back and the captain let them have at it. So, obviously the pirates were blown away. Having spent time on ships I can only imagine what that would be like, considering that the smallest weapons I ever saw were 50 caliber machine guns. That would seem to be a fairly effective approach.
Also interesting to note, the United States first major foreign crises after the revolution were with north african pirates, one of the primary motivations for the creation of the peacetime navy.