errrr
American Troops are still in Korea because of the threat of a North Korean invasion. The same goes for germany and Europe for fear of a Russian invasion. Essentially those locations are leftovers from the Cold War.
I'm not quite sure why Iraq, though. I don't really think anyone knows. WMD and being a harbor for terrorists, I guess. Except WMD never existed and now the terrorists have a reason to be in Iraq, i.e. to attack US Troops.