Those look like the Fall Webworm, a cousin of the springs Tentworm. Because these wee buggers appear fairly late in the growing season they really do little harm to the trees they infest, just cut down on how many leaves you get. The nests are unsightly, and this offense to your eyes is worse than the damnage they might do to any trees. Early on, less then about 5 weeks of age, spraying Bacillus thuringiensis - Kurstaki will help control them, ripping open the web (this allows the many predators of them access) can help. Pruning the branch the wee buggers are on can be done, although that may create more problems. Burning the nest in place is not a good suggestion since it can cause many more problems (major brush fires have been started by doing this) are created and the heat from doing that could damage the branches more than the webworms would.
Neem Oil products can be used to control these wee buggers as well as a numbr of other products, many of which are very broad spectrum poisons that will kill off the predators quicker then they will kill off the webworms.

Here is a link that might be useful: About fall webworms

One way to control them is to use a stick and rip open the webs. The birds love them.

two things we did
1) prepare a small camp fire in a safe spot, away from dry materials; cut the branch with the web intact, throw into the fire
2) spray Sevin on it

We had a huge colony of these webs on all wild cherry trees on the property, took 2 seasons of combinations of #1 and 2 , this year - I dont see them at all. If I see it, I will go with #2

Good luck

Thanks for the helpful responses. I think I can cut the limb fairly easily, but I may open the web first to see if the birds can do the work.

Not only birds, but other predators and parasites will be able to get at the caterpillars. There are lots and lots of helpers out there.

Whatever you do, don't use the Sevin. That's the chemical most famous for creating a population INCREASE in pest insects and mites.

Since the Fall Webworm are larva of a moth they grow, pupate and become the adult motht hat lays more egggs the become the webworms that infest your trees every year. Some places can have 2 generations of them.
Integrated Pest Managment means learning about the target and then if it is necessary applying the least toxic mthod of control first. IPM is not about grabbing the most toxic substance that exists and is readily available, Carbary (Sevin), and spraying that around because that will kill off the predators of the webworms as well as the webworms.