Clematis, climbing roses, wisteria, silver lace vine, honeysuckle, trumpet vine, virginia creeper, possibly hops...

Also see this website: http://www.evergreengardenclub.org/garden_articles/Perennial_Vines.html

I will say that you might need to be careful planting against your back fence. My very annoying neighbor actually sprayed herbicide on my side of the fence, killing just about everything I had planted there, including a couple of climbing/vining plants that were for privacy.

You can also try tall bushy plants instead of or in addition to vines and climbers.

I don't know if vines will help, the dogs would likely bark at any noise.

Anyway, I have a lot of clematis here. They do very well in the climate - Jackmanii with the purple flowers thrives here. They take a good 3 - 4 years to get going, but when they do,

Proceed with caution!

I have a Virginia creeper that was planted by the former owner of my house. My former neighbor didn't like it. It expanded its territory to cover his side of our shared privacy fence. He asked me to keep it in check and it was a chore.

That said, I really like it. It is hardy and leafy, and turns bright red in fall. It also produces berries for the birds.

I guess the question is WWTNT? (What will the neighbors think?)

Steviewonder

I love my Silver Lace, even if it can be invasive. My neighbors love it too, not only for their own privacy, but because they get to enjoy the blooms as well!