These five (and a half) principles are generally seen as the ones available, but not every nation thinks they’re all appropriate. In fact, prior to Sept. 11th, the U.S. condemned the invocation of Passive Personality and wasn’t a big fan of Universal jurisdiction either. Remember that what usually happens (outside the extradition context) is that the Court system that’s actually going to prosecute the defendant makes the decision as to whether its own jurisdiction is appropriate.
It’s important to note that the exercise of any extraterritorial jurisdiction is controversial and there’s often a period of negotiation between the State Department and the country where the alleged criminal is located.
What hello has cited as the Sec. 403 principle is really an invocation of the Territorial Principle used extraterritorially – to prosecute activities, legal where they were transacted, which have effects in the U.S. For instance, the U.S. has used this to enforce antitrust laws, which are a lot more aggressive in some ways in the States than in, for instance, the UK. There’s a famous suit against Lloyd’s of London wherein certain partners of LLoyd’s made deals in England that were legal in England but, if done in the U.S., would have been illegal here. Since the deal had effects on the international insurance market and therefore U.S. prices for insurance, the U.S. court system felt it had the power to prosecute Lloyd’s on this basis.
Again prior to Sept. 11th, the invocation of Universal jurisdiction was also very rare – although it was sometimes mentioned in the case of genocides, I think most legal opinion was that it wasn’t appropriate for that. The justification for Universal jurisdiction is that the crimes to which is applies are those which threaten not society or world peace, but the very fabric of the system of international relations. The theory being that as long as international commerce and congress are available, you can work out any other problems. Piracy is the big area here, because when the trade and communications routes are unsafe international relations break down. Therefore any country should be able to stop it, regardless of whether they have a specific interest in the particular cargo or persons involved.