All of the local members of Piciformes are in one family, Picidae (woodpeckers and flickers). They are presented in alphabetical order by genus and species.
Northern Flicker (Colaptes auratus)
Like their close relatives the woodpeckers, flickers brace themselves against trunks and branches using stiff tail feathers. Male Northern Flickers have red "moustaches"; females have tan-to-gray ones you may not notice. Both have tails with a lot of red when seen from below. The final image, of a feather, shows why Northern Flickers in this part of the country were once known as "Red-Shafted Flickers."
Ladder-backed Woodpecker (Picoides scalaris)
Key characteristics to look for: the banded black and white back and the light face marked with black lines. If the top of the head is red, the individual is a male. Two of my photos are of a female hanging on desert willow seed pods and pecking her way into them. A few days later, I caught a different female trying to peck her way into pecans.
Downy Woodpecker (Picoides pubescens)
Please see my comments on Hairy Woodpeckers, below. Downy Woodpeckers are distinguished (barely) by having dark spots on their white outer tail feathers and by having fuzzes of white down at the bases of their upper beaks. You can see these attributes in my photo from November 2020. Downy Woodpeckers have shorter beaks, proportionally, than Hairy Woodpeckers, but lotsa luck estimating beak length when you actually see a bird.
The two photographs from May 2020 illustrate how challenging it can be to distinguish the two species. In one photo you seem to have a good view of the outer tail feathers, and no black spots are to be seen. In the other photo, of the same bird, the actual outermost tail feather isn't hidden by the next one in, and two spots (indicated by arrows) appear. Same story with my photo from January 2021. It shows the spots, but in most of the photographs I took of that bird, the outermost tail feathers were similarly concealed.
Hairy Woodpecker (Picoides villosus)
If you don't see much difference between Downy and Hairy Woodpeckers in my pictures, I'm not surprised. When it comes to these two species the differences are so minor, I'm often unsure of my IDs. Hairy Woodpeckers have longer beaks and lack dark spots along the white outer edges of their tails.