Looks like Myrsiphyllum asparagoides, Florist's Smilax.

I had considered a deciduous holly, too, suja, but the leaves and the shape of the shrub didn't match up. I'm afraid it is autumn olive. I had also considered this, but the leaves didn't look quite right in the pictures I had looked at. After reading sam_md's post, I looked at some more pictures, and the berries are a perfect match, right down to the little brownish spots on them. I checked while I was out walking today, and the undersides of the leaves are indeed silver. Mystery solved, I guess. Too bad. It's really a very handsome plant. I've always read it was a very invasive, undesirable plant, but I can see why it gained popularity when its planting was encouraged. Unfortunately, this particular shrub is located on private property, so I won't be able to chop it down. At least now I'll recognize it if it shows up on my property. I can add it to my list of things to eradicate, along with oriental bittersweet, mile-a-minute vine, garlic mustard, . . . The list never ends. Thanks to both of you for your help.

Yes Camp, that's not the kind of "trip" one should take, being more of a deleriant than a mind-opener. What's odd though-and here I go again with my hawthorn story-the initial stabbing took place while in the back of a truck loading the B&B plant for travel. Through a layer of newish Carhart overall pants, through another set of regular pants, and on into my femur. Folks at the ER laughed at my attempts to self-doctor! I wish that had been the last of it between me and that plant but in truth, years later, when it was firmly established in a planting, it got me again, but good. My woods is full of some kind of Hawthorn. Not very good at IDing these things and besides, they're as promiscuous as oaks, if not more so. At any rate, I tolerate them-along with the prickly ash-but certainly don't favor them when it's down to one of them or a pathway or something! +oM

Google "asparagus fern".