Beech Blight Aphid (Grylloprociphilus imbricator). As the name implies, these critters attack the stems of beech trees and suck the sap from them. Very large numbers on small twigs might cause damage or death to the twig but they do not impact the general health of an otherwise vigorous tree.

They are also called the Boogie Woogie Aphid since they will wag their "tails" in unison if the twig is jostled.

Note: These were found on the branch of an American beech tree.

Thanks to Jennie for identifying this plant.