Perhaps Cornus racemosa.

If definitely wild look at which species occur in your area. One like this will be in this subgenus:

http://www.efloras.org/florataxon.aspx?flora_id=1&taxon_id=318093

Cornus racemosa looks right to me, too.

Thanks for the comments. Amazingly, my walk yesterday took me to this wild area and this dogwood had such nice berries, but didn't look like the other wild dogwoods on my property, (except I forgot about the one that I had planted right by my entryway! )

Yes-exactly the same Grey Dogwood I look at every day going in and out the door.

Of course I would not have made the distinction without the outside help from the rest of you. Thank you all very much.