These are schwarzenberen (solanum nigrum), a European nightshade distantly related to tomatoes. The berry is tiny and pretty tasteless, a tiny bit sweet and acidic, not at all what you would expect from a "berry." Rather like its cousin in that sense. It's also chock full of seeds. I first grew them two years ago, and last year was their first chance to naturalize. They did, with a vengeance. Now they're all over, and I love it. The biggest plant is in my garden.(naturally) but they also love the dry west end and the fringe along the shade shadow of the big
ash tree, where the fruit tree hedge will be.
The fruit, as I said, is tiny. It grows in clusters that don't always ripen at the same time, so I'm going to do some generational alterations. :)
The seeds I saved are from the very largest of the fruits. Most came from the same plant, but I took the largest fruits from the other plants as well. First to ripen, largest. Next year I'll plant these in a dedicated spot and again take seeds from the largest. It may be a tradeoff between size of the fruit and quantity. Once they're large
enough to handle easily I'll start working on flavor and maybe someday I'll get ambitious and try to work on the number of seeds!