How about trumpet vine? Mine is very well established (was here before I bought the house) and has gone clear under the driveway to a garden on the other side. It goes into the lawn, but there it's mowed down weekly so isn't a problem.
I didn't know some of these things - like cutting it down in the spring (already too late for that this year, but maybe I'll do it anyway). I've tried Roundup on the shoots in the other garden without success. I'll give boiling water a try there.
Creeping Bellflower should be on this list too as it is also awful and people let it go to seed and spread horribly. It is a pretty flower but takes over completely as the tap roots are nearly impossible to eradicate.
We have problems with half of these and, like Echo's Garden said, trumpet vine. But the worst if all for my area is multiflora rose! We've been trying our best at eradicating the plants for the last 14 years! It is choking off all our native trees and shrubs left and right. It wouldn't be so bad if the scrambling didn't have thorns all over them.