There's an article recently posted on the International Law Observer site about what to do with captured pirates (downloadable as a PDF). Written by American jurist Michael Passman, and originally published in the Tulane Maritime Law Journal, it details various legal codes that may apply to suspected pirates, including the Geneva Conventions.
From reading Passman's article, I found it particularly intriguing that the U.S. Municipal Piracy Statute (18 USC 1651), which originated two hundred years ago, states that "Whoever, on the high seas, commits the crime of piracy as defined by the law of nations, and is afterwards brought into or found in the United States, shall be imprisoned for life." (Though it should be noted that another, more recent statute, 18 USC 2280, offers a sentence of "not more than 20 years", plus a possible fine, albeit for acts of piracy that do not include murder. Killing a mariner can result in a pirate being sentenced to "death or imprisoned for any terms of years or for life."
Though the United States has not prosecuted anyone under the Municipal Piracy Statute in a century, it's still on the books, meaning it could be applied should Somali pirates be captured by US Naval forces.