No British citizen has ever been extradited to the United States for a copyright offense. But Richard O'Dwyer, the 23-year-old college student who ran TV Shack, may become the first.
As I understand it, the charges aren't that his (very popular) site actually hosted the copyrighted content, but that it served as a directory of links to other servers online where those downloads could be found.
Torrentfreak has more on the legal battle. The lawyer for accused hacker Gary McKinnon, whom the US would also like to extradite for prosecution, is representing O'Dwyer. They lost their first round in the extradition case today, and have 14 days to appeal.