What are some examples of modern stereotypes of Native Americans?
Most stereotypes of Native Americans are rooted in a lack of historical awareness. Some are negative, others less so, but they all have the effect of flattening Native Americans into something less than what they were. A particularly pervasive stereotype is that all Indian peoples were nomads, who lived in tepees and followed herds of animals. While this is true of some (not all) Plains Indians, most Indian people lived in highly stratified societies, practiced settled agriculture, and lived in permanent villages. The idea that Indians didn't "improve" the land through farming was largely a fabrication perpetuated by whites who wanted the land for themselves.
Another myth is that Indian methods of fighting were particularly brutal compared to whites. This does not hold up under scrutiny either. While many Indian peoples practiced ritual torture of captives, and went to war quite often, most did not usually engage in the type of "total war" that Europeans did. In other words, they did not usually destroy crops and other people's way of life. They fought wars and took land from each other, but their wars were usually fairly limited, and usually took the form of raids on enemy people.
Other, more "positive" myths often take the form of what anthropologist Sheperd Krech has called the "ecological Indian" who lived in harmony with nature, never took more than he needed from nature, and had no concept of land ownership. This stereotype is closely related to the old "noble savage" construct used by many European thinkers like Michel de Montaigne and Jean-Jacques Rousseau. While it seemingly positive, As historian Richard White once observed, the idea that Indians, unlike other people, left no mark on the land they lived in "demeans Indians. It makes them seem like an animal species, and thus deprives them of culture."
The most important, broad stereotype to reject historically, however, is the idea that we can even speak of "Indians" at all. Native Americans were a very diverse group, separated by geography, culture, religion, and politics. They were, in other words, human.