Agree with gonebananas, looks like Suriname cherry, but do check to make sure. Will make a good jelly, if you get can get enough of them.

They look like wild grapes. We used to make the best jam from them when I lived in Kansas many years ago.There was a small river and they grew along a fence line. I am no expert, so you should not eat them until someone tells you for sure. If they are wild grapes, lucky you! Maybe a neighbor would know, and others on gardenweb have more experience with wild berries than me.

Thanks everyone. They grow in my backyard and they look cultivated. They don't have thorns or anything like that. I don't have pictures of berries but if you know how red currants look like they are very close to it. May be it is some sort of hybrid of red currants and something else? I wouldn't eat them if they were wild but I assumed they were part of edible landscape the previous owners had.

Thanks for the suggestions. I forgot to mention the berries were spherical and always shiny, even when black, so that rules out both Capsicum & Viburnum species shown. I think I would have remembered if the berries were purple at one point, too, so that mostly rules out Capsicum. I did find a pic of (supposedly) Solanum nigrum online that had red berries, though there were conflicting captions on the photo. Maybe my mystery bush was Solanum nigrum after all, or maybe some other species of Solanum. Here is a link that might be useful: