Much of the Western U.S. is public land; National Park Service, Forest Service, or Bureau of Land Management (BLM). As noted above, you can legally camp anywhere on Forest Service land unless it is otherwise posted. The same goes for BLM land. You can sometimes camp on National Park Service land outside of an established campground but it varies between the different parks and monuments. In some of the National Monuments here in Arizona, it is illegal to even walk off the established roads because of they don't want the public to disturb sensitive prehistoric ruins.