Many Pagans like to claim not only Celtic heritage, but also Native American heritage. Even those who do not claim any heritage still enjoy picking and choosing and adapting the beliefs of some N.A. people to suit their own practices.
Some examples of this are the Medicine Wheel, sweat lodges, vision quests, and totem animals. The Medicine Wheel is symbol for the wheel of life. It involves the four cardinal directions and four sacred colors, which resonates with circle-casting Pagans and Wiccans.
Medicine wheels are constructed by laying stones in a particular pattern on the ground. Most medicine wheels follow the basic pattern of having a center of stone(s), and surrounding that is an outer ring of stones with "spokes", or lines of rocks radiating from the center. Originally, and still today, medicine wheels are stone structures constructed by certain indigenous peoples (that would be Native Americans, or American Indians, if you prefer) of North America for various astronomical, ritual, healing, and teaching purposes. More recently, syncretic, hybridized uses of medicine wheels, magic circles, and mandala sacred technology have been employed in New Age, Wiccan, Pagan, and various other communities and spiritual paths throughout the world.
Another popular tradition that has been adopted is the sweat lodge. The sweat lodge is a ceremonial sauna and an important ritual used by various peoples of North America. The Lakota ritual seems to be the most common. Basically, stones are heated in a fire. A dome-like shelter is constructed. Participants sit around a pit and rocks are brought in and water is poured of them. The rituals and traditions vary from tribe to tribe. Some sweats are silent, while others involve singing and praying. For more information, please visit http://en.wikipedia.org/wiki/Sweat_lodge.
Somewhere along the way people got the message that being eclectic meant borrowing a little bit of this and a little bit of that from various spiritual paths, and weaving them into something very stylized and very personal, into something from which the original parts could not be distinguished.
The use of various N.A. traditions by non-native peoples is very controversial. I won't go into my personal opinion of using most of these traditions, but you can probably guess my position. If it is done with respect and a lot of studying, and it involves someone who actually knows what the heck is going on, it can be fine. Unfortunately we run into a lot of people who claim to be 0.64273411 percent Cherokee or Lakota (this are currently the most commonly claimed) and consider themselves an expert on the ways of ‘their people'. It can get embarrassing.
Dream catchers are quite popular in the Pagan/Wiccan community and can be purchased at pretty much any New Age shop. People whose spiritual paths are heavily influenced by N.A. peoples tend to wear t-shirts with wolves on them, bear fetish necklaces, leather vests, and bead-and-feather hair ornaments. . They usually take a name that has "Wolf", "Bear" or "Eagle" in it. It can be even harder to dance to their drumming than to the other bardic circle musicians'.