Invasive Himalayan blackberries are a big problem in Oregon. After spending a day hacking back vines that suddenly showed up DD's urban yard, I'm wondering if there is any organic method of permanently discouraging this beast? Would a vinegar spray work?
SnowlineRose - If this blackerry is on somekind of "Invasive Species" list then possibly your neighbor will have to get rid of it. I don't know about such things, but your local extention agent should know.
Even if a plant is so horribly invasive that it winds up on a state's noxious weed list, they still don't go around to people's yards making them get rid of it. They just ban it from being sold anywhere in that state. So I wouldn't count on the "plant police" showing up anytime soon to make them remove it--if you don't want it in your yard I'd talk to your extension office about how deep of a barrier you'd need.
Some areas though have rules about keeping your yard up--so if your area has a homeowner's association or any other sort of rules along those lines you might be able to complain and have someone force them to clean up their yard and keep it a little nicer.
I just got back from a driving trip from my 'hood (SF bay area) through Oregon and to Seattle. I asked my husband, the Oregon native, if people go blackberry picking during the summer. He said you have to be careful because people spray them to try to keep them at bay.
The irony is that I would LOVE, LOVE, LOVE a whole grove of blackberries, but it is just too hot and dry to get much traction here.