As much as it pains me to say it, posters like Diogenes who are wondering about U.S. legal authority here are asking exactly the correct question.
First, power is not the same thing as authority. There is no question the U.S. has the power to arrest Sadaam and try him. Heck, there is no question that the U.S. has the power to summarily execute Sadaam by feeding him to wolverines.
But that doesn’t mean the U.S. has the authority to do so. The idea of holding a trial necessarily includes the idea that the court has jurisdiction to try the case and that there is some sort of recognized law that the defendant is being charged with breaking.
The problem here is that Sadaam hasn’t actually done anything done wrong that the U.S. can claim jurisdiction over. On the international front, there is no evidence that Sadaam had WMDs so there is no evidence that Sadaam and his government actually did violate the terms of the treaty that ended Desert Storm I. Even if they did have WMDs, he certainly never used them. I should point out that it would be a bit stiff to execute a head of state because his country violated a U.N. resolution. After all, countries violate Security Council resolutions in large or small ways 50 times a day.
So if you’re going the war criminal route, you have got to push all the way back to the invasion of Kuwait or, perhaps, the Iran-Iraq war. This is pretty weak. Both conflicts ended with treaties (as opposed to unconditional surrenders, unlike WWII) and neither treaty says anything about war crimes.
More to the point, the U.S. doesn’t have any standing in either conflict. Apart from occasionally stirring the pot, the U.S. had nothing to do with the Iran-Iraq war – it certainly was not a combatant. As for Gulf War I, the U.S. spearheaded things but it was, in effect, working for the U.N… Kuwait probably has authority to try Sadaam but it’s hard to see how the U.S. would. It’s also kind of an emotional let down. The invasion of Kuwait is really old news. Having said that, the invasion of Kuwait is the best legal cover for an interational tribunal.
All the rest of Sadaam’s crimes are domestic rather than international, and neither the U.S., nor Russia nor any other member of the international community (except maybe Sweden) is going to go down that road. Sadaam will be the U.N.'s Secretary General before say, China, will allow an international tribunal to try a head of state for his conduct of domestic affairs.
So the best option is to let the Iraqis try him for crimes committed against Iraqis. I predict that’s exactly what you’ll see, precisely to avoid the problems detailed above.
BTW, here’s an old semi-official statement detailing Sadaam’s crimes. As you can see, they are almost entirely domestic.
http://www.fas.org/news/iraq/2000/09/iraq-000918.htm