This is a Brown Creeper (Certhia americana). The quote at the beginning of the Birds of North America account is a perfect description:
“The brown creeper, as he hitches along the bole of a tree, looks like a fragment of detached bark that is defying the law of gravitation by moving upward over the trunk, and as he flies off to another tree he resembles a little dry leaf blown about by the wind.” 1948)
Brown Creepers are small (12–13 cm long) tree-climbing passerines. They're the only representative of the treecreeper family in North America. Their coloration is cryptic, brown above with white/buffy spots and streaks and generally white below.
Note the long, thin decurved bill (for gleaning insects and spiders from furrows in the bark), distinct supercilium (eyebrow stripe), long tail (used as a prop against the trunk), and long curved claws (for grasping pieces of bark).
Creepers forage in a predictable pattern, starting at the base of a tree, climbing up to near the top, then dropping down to the base of a different (or the same) tree to start again.
Their high-pitched calls and songs are distinctive once you are familiar with them — a sibilant tsee note or a longer song tsee-tuti-sedu-wee . You can listen to them here.
Amazingly, creepers build hammock-like nests between the trunk and a loose piece of bark.
Almost everything about Brown Creepers is an adaptation for living closely with large, old trees.