UPDATE: Jonathan writes in the comments:
ICC prosecutions are controlled by the prosecutorial staff rather than private parties. Anyone can file a complaint with the ICC, just as anyone can walk into a police station in the United States and report a crime, but the complaint won't be pursued unless it's deemed worthy by professional prosecutors.
fair enough, but I'm still leery. My gut feeling is that the President should be ultimately held accountable to the American people, and not any external body.
Personally, I would favor an ICC that was limited to jurisdiction over governments that are not democratic only. Also, I think that the jurisdiction should be limited to government officials only, NOT military enlisted personnel.