The most common woodpeckers found in the backyard are the Downy, the Hairy, the Red-Bellied and the Northern Flicker. Some parts of the country have other species, including the mighty Pileated and the maligned Sapsuckers.
All are cavity nesters and will readily adapt to a nesting box. Be careful when selecting a suitable box. Woodpeckers would not have much interest in an elaborate Victorian mansion style nesting box. Instead they prefer a utilitarian wooden box with an adequate sized entrance hole.
In the wild, it is common for woodpeckers to find a cavity with a small entrance hole and to then work it up to the right size. A metal guard on a Downy Woodpecker nesting box helps keep the Hairy Woodpecker from staking his claim. A small bag of wood chips helps the woodpecker get started with the nest, mimicking the natural chippings that would fall in the hole during the parent's excavations.