is this black nightshade?
This does look like black nightshade. Since the picture does not let me see a good view of the flower or the leaves I can't be certain. The unripe berries in your photo do look like the ones in the following link. http://oregonstate.edu/dept/nursery-weeds/weedspeciespage/black_nightshade/black_nightshade.htm This link shows several pictures of black nightshade and should give you something you can compare your plants to and to decide. Yes I would (and do) remove these plants when they show up on my property. The leaves and fruits contain toxic chemicals and it is a prolific reproducer. Your certainly want to get rid of it prior to the berries ripening and releasing their seeds.