Strictly speaking the red part is edible but all other parts of the tree are highly toxic, so, unless you are literally starving I would leave them strictly alone.

Two pictures of the same thing and not close enough to tell what it is. Here is a link that might be useful: Your picture

Looks like Beautyberry (calicarpa americana). I think wine can be made with them. They may be edible, but I haven't ever eaten them. Harry Here is a link that might be useful: Beautyberry

Hey everyone, thank you all for the helpful comments! These definitely aren't blueberries--they are quite firm despite the dark purple color and they do not have the same type of indent on the end as most blueberries (where the flower used to be). I was thinking it might be either a prunus or some kind of a serviceberry--but just wanted to make sure this wasn't something like a (poisonous) buckthorn.... Later this afternoon I'll cut one of the berries open to see what is inside, and maybe that will help narrow things down. The color in the picture is fairly accurate--fruit are dark purple, leaves are dark green with red/purple. This is some sort of an ornamental bush, too--someone planted it intentionally for looks, judging by the rest of the yard and the bush itself.