This is Smilax rotundifolia, also called roundleaf greenbrier. It's common enough out here, but I've never been able to identify it until now - these blue berries are a dead giveaway.
It's also called Catbrier. We have the variety that has a few thorns [hence the name greenbrier], but not tons of them. Some of the Smilax species have stems covered with bristly thorns. It's worse than the multiflora roses to deal with and almost impossible to get rid of.
These berries will hang on all winter and are an important source of winter feed for birds and animals. [Which will help me rationalize my decision to just let them be.]
Here are more pics of the leaves so you can see what they look like during the summer. The leaves remind me of a fleshy sort of clematis. They're really pretty.