I also have a view problem.
My neighbors (1) have a giant ugly motor home parked in their driveway where all you can see is the moldy roof when looking out our guest room window and (2) they stuff total crap in between the slats of the fence and stack/lean all kinds of junk up against it that i have view of (it is one of those shadowbox styles). They are really nice people but they have an obvious problem with keeping and collecting total junk (deflated footballs, old fake poinsettias, jars of odd liquid, a "Santa Stop Here" sign they prominently display at the head of the driveway year round even though it looks like it caught fire at one point, pieces of rusty metal parts, old windows, and on and on and on).
The junk can mostly only be seen in my backyard along maybe a 20 or 25 ' section of fence. I've plated plants that get big on some parts, but other parts I can't because there is already a large tree there that things can't grow under. I was wondering about stapling some kind of screen to the fence on my side but I think it would look strange in only a section of the fence (and might look tacky just overall).
I don't know what to do :(
That sounds so awful. I think that would really be upsetting to have to see every time you step out in your yard.
I'm not big on confrontation, but you say they are nice people, so have you tried asking them if they could maybe clean up the yard a bit? Just tell them nicely that it's not very nice to look at and that you're worried that it might be an attraction to wildlife like skunks and snakes. This would work better if you've got smaller kids that you'd let play in your back yard - a small white lie about seeing a snake coming from one of their piles, and that you're worried about your kids being able to go play in their own back yard. If you're game, you could even offer to help them clear out some of the junk. The worst they could say is no, but maybe they'll think about it later and get embarrassed enough to do something about it. (but if you think they'd get violent about it, forget it!)
My dad was this type of neighbor, and I feel so bad for the folks that lived next to him - his yard was a mess of overgrown/dead trees and weeds, and he had at least 12 mowers in various states of assembly with trash and junk scattered throughout, and an old popup camper with a broken top/axle that had a tree growing up through it... and yes snakes. He had mice all through the house, and they attracted snakes and one of the neighbors that has a 5 year old couldn't let her play in their back yard since he had killed so many coming over for a "visit."
A fast growing, shrub like red tipped photinia might work. They can go under trees even if you can scrabble out a hole large enough to drop a root ball in. Those suckers are fast, evergreen and get huge and they can be pretty:
http://davesgarden.com/guides/pf/go/1740/But they also can get stunted growth from bugs and subject to fungus.
Crepe Myrtles (there's tree and shrub varieties) are also fast growers and would be good at camoflaging an ugly view. They will drop spent flowers and pods, tho so can be messy.
I'm not sure where you're located so these might not work for your zone. You should go to a local nursery (one that has actual gardeners that know what they're talking about) and see if they have any suggestions.
You don't say how high your fence is, but where I live, 6-8 foot fences are standard, and I've seen even taller. If you don't have a really high fence, might want to look into that as well since at least then if might hide the junk better. Like these:
http://www.google.com/imgres?imgurl=http://www.mossyoakfences.com/images/original/products/wood_privacy_fence_1.jpg&imgrefurl=http://www.mossyoakfences.com/fence_products.php&h=1553&w=2070&sz=2857&tbnid=j2B3pRskfQGf4M:&tbnh=92&tbnw=122&zoom=1&usg=__mwhX9tXRwUHXGH4EQvfjGqcQDTE=&docid=JuIsqol7j6INkM&sa=X&ei=M1vcUYjdN4W89gTeq4HgDA&ved=0CGkQ9QEwBQ&dur=2815#imgdii=j2B3pRskfQGf4M%3A%3BVtwofKgNsZlmNM%3Bj2B3pRskfQGf4M%3AIf you wanted to put in a privacy fence, you could tell them that you're going to do this and that you'd need them to shift their stuff off the current fencing and to please not stack stuff on it it once it's in there...
again, tho, you have my sympathies. It is so difficult to deal with hoarders and their junk and trash.