The word Polychrome is used to describe the use of multiple colors in one item, usually in regards to pottery, sculptures and architecture.
The Hopi Indians have made polychrome pottery for centuries. The pictured snake bowl is a old tribal bowl, not one you would find in today's tourist shop. The bowl depicts a snake swallowing it's tail, this is a mythical idea of the Native Americans that represents a circular view of the Universe. Most of you have seen the Lion King, it is the same concept as the "Circle of Life". This bowl is probably from the early 1900's or even older. The value of this bowl should be in the thousands but what it is worth and what it will sell for are generally two different prices.
The second photo is of a vase or olla with a feather and geometric design, it is from the 1940's era. This bowl sold for $300 on eBay last week.
Tourist shops do sell artwork of Polychrome Pottery from today's Native American Artists. Most are dated and signed by the artist and they tend to be rather pricey but not near as valuable as the vintage or tribal items.
If you enjoy decorating with a Native American theme this type of pottery is a must in your decor.