A few days ago my children and I discovered these unknown plants growing near our back fence and in a nearby flower pot. The purple flowers look so delicate and I am inclined to leave them where they are, but first I would like to know whether they are a weed or a wildflower.

Does anyone know what they are?

Update: Our unknown flower has been identified by Dawn (please see comments) as Herb Robert. More information about this annual can be found here, Noxious Weed Control Board.