Hairy Woodpecker (Dryobates villosus)

hairy above, downy below

Red Bellied Woodpecker (Melanerpes carolinus)

Downy Woodpecker (Dryobates pubescens)

small bill, less than half the width of the head, and narrow

females have no red on head

outer tail feathers with black bars on the white (not always visible)

fluff on "nose" fluffier in downy than in hairy 

male red spot can be continuous

male red spot can be divided by black

young downies have reddish foreheads, but I'm not sure if this is that or just a male in a weird position