I think these are aphids. They appear to be exoskeletons or dead? There's no response when I shake the branch.
I can just remove them with my fingers? Should I be on the lookout for a more mature form of the insect?

If it is like a hard dome like structure on the branch then it is scale. You might also have black pots on the leaves below them which is fungus from their excretion. They are not a welcome pest. If you can scrape them off do it then use need oil to coat your tree and suffocate the rest.

these are normal aphids. And yes. Alive. They do not respons to branch shaking. Whipe them off with your hands or a strong waterspray.
This is a mature form of the species.

KILL THEM ALL !!!!

Use systemic pesticide like bug clear ultra that will kill them plus soak into the plants vascular system meaning any bug for 3 weeks will be poisoned aswell and it does not hurt the plant before you ask.

Thanks for your responses everyone. I had never encountered black aphids before. Really the only time I've seen aphids they were white and it was a large infestation in field trial where we were testing the uptake and efficacy of pesticides for chewing insects so we couldn't do anything for them except release 1000s of ladybugs every week.
I hope the weather (and my homework) lets me get outside and take care of this today. I discovered this mess just before leaving for class last night.

Haha lucky you.

My plums and roses get harassed by aphids april through october.

They die off in winter. Spray spray spray. but not too much. if it` just a few use your fingers.

as mentioned in another post a good insecticide will rid them for a few weeks.