One of the most important things to keep in mind while traveling and visiting historical sites is to keep your hands to yourself. You shouldn't touch things that are historical, especially if there are specific signs requesting otherwise. Many tourists traveling abroad do not take these signs seriously, and they can actually cause a decent amount of damage to historic sites and museums or such as a result. Always be vigilant!
This is not something that specifically applies to Americans, however. It seems to be a general issue with tourists from all different places not following the rules.