I planted trumpet vine in 2004, before I started this blog. Apparently, I made no note of its variety, but I did find an old post that indicated I waited five years for it to bloom, primarily because it was not getting enough sun. The idea behind planting this obnoxious vine was to obscure the chain link fence, which it never did to any satisfaction. However, it did pop up all over the place, causing much cursing and consternation.
The shade-providing silver maple is gone, as is the chain link, replaced by a privacy fence, and yet this thing still survives. I will probably regret it, but I am leaning toward letting it be, just to see if I can control it and if it can provide some nice cover for the fence. It is native, although not in Indiana.
Another pernicious vine is Virginia creeper. This corner of the yard has been cleaned up somewhat, after I ripped a mile or so of Virginia creeper off the serviceberry (while obsessively counting leaf clusters - no poison ivy). Virginia creeper turns a lovely scarlet in the fall, so I'm letting some grow on the fence. It too is native.
I think my rule of thumb going forward will be to let these vines climb the back fence (FOR NOW) because the area behind the fence is technically my property. Also, the view of the neighbor on that side is blocked by his privet. But I think I will keep the side fences clear of climbers so I don't have to worry about them encroaching on those neighbors' yards.
I've also been pulling down what I think of as wild grape vine. So far, it has been growing on the side fences but not the back fence. Unlike the others discussed here, it is not a very aggressive plant, at least not in my yard. I think it is not native, so I may continue to curtail it. My yard, my (arbitrary) rules.