I have this bird at my feeder in Southern New England. Why they are called "red-bellied" is beyond me because it sure is not a distinctive feature. They are fairly common up here. Wacka-wacka-wacka.
A common woodpecker over much of the South, the Red-bellied is scarcer farther north but has expanded its breeding range northward in recent decades. Like most woodpeckers, it is beneficial, consuming large numbers of wood-boring beetles as well as grasshoppers, ants, and other insect pests. It also feeds on acorns, beechnuts, and wild fruits. It is one of the woodpeckers that habitually stores food.
Breeds from South Dakota, Great Lakes, and southern New England south to the Gulf coast and Florida. Northernmost birds sometimes migrate south for winter. Inhabits open and swampy woodlands; comes into parks during migration and to feeders in winter.
The Red-bellied Woodpecker competes vigorously for nest holes with other woodpeckers, in one case even dragging a Red-cockaded Woodpecker from a nest cavity and killing it. But it is often evicted from nest holes by the European Starling. In some areas, half of all Red-bellied Woodpecker nesting cavities are taken over by starlings.
More about the Red-Bellied at CLO