Lilac doesn't do very well in shade.

Grapes often create thickets and would do a good job of covering a fence and would probably eventually cover the junk too. They might pose a problem for your trees if they are not kept under control though. Virginia creeper could work similarly and be less of a threat to trees. Also Greenbriers (Smilax spp.) and Raspberries (Rubus spp.) would form a thicket around the fence but might annoy the neighbor.

Come to think of it, Purple Flowering Raspberry (Rubus odoratus) would be a really nice addition to a woodland and might do the trick.

I also have a fence at the back of our woodland that is not problematic but would look nice with a vine covering it. It is quite shady and we have two large black walnuts on the property and I'm sure many more immature trees in the understory somewhere.

I considered clematis, but was unsure if they would be prolific enough and if they would flower in the shade. I happen to love wisteria and trumpet vine, but I think they are a no-no in the woods. Morning glories might be nice, but probably wouldn't cover the fence enough to hide the junk. They are also probably a no-no in the woods.

My annabelle hydrangeas do well at the woodland border, but may be too slow to grow to create a screen, and may not flower as well in the shade. I also have elderberry bushes, again at the woodland border, but they do well in quite a bit of shade. They spread though.

As far as grasses, I have recently planted miscanthus in my front yard to hide a stump. They are in part shade, but need some sun to really thrive so may not be appropriate for the shady understory. They do get pretty tall though.

I guess I really don't have any suggestions that would be 100%. The only other thing I can think of, would be a clump forming bamboo. That may work really nicely- just make sure it's clump forming and doesn't invade your woods.

In short, good luck ;)

One thing to consider is that if you do go with a vine and the vine gets over into the neighbor's junk, he may spray it with a systemic herbicide and kill your screen. If you want to plant something right at or on the fence and don't have easy access to the other side for maintenance, I'd recommend staying with some type of shrub or maybe even a solid panel fence.

Listing where you live (city or part of the country) might lead to better answers about what would work in your area. Your hardiness zone alone only gives part of the story.

Please, please, please avoid bamboo. Even the so-called clump forming can be a problem and disasterous to our native woods!

Cyn, can you describe how a clumping bamboo (non-invasive type of course, as many are) would be likely to cause a disaster, especially with reasonable care?

I'm not saying it would necessarily be the best solution, but I don't see the need for such alarm if non-invasive, clumping varieties were used.

The OP could even use native bamboo. It does get out of hand and can become weedy but since they are native would not be considered invasive even if they spread a mile.

Brandon, It is difficult for most to be absolutely sure that what they are buying is clumping and I have my doubts that there really is any such thing-clumping just spreads more slowly. I know people who bought "clumping bamboo" only to have it spread like crazy. I spent years trying to get rid of bamboo that was here when we moved into our house (and don't believe ANYONE who tells you it is easy to eradicate) and had choked out everything else in the backyard, so I have an intense dislike for and distrust of bamboo. That said, it is beautiful. I just don't want it anywhere near my yard. It keeps trying to move back in and I keep fighting it. Not a pretty sight!