What plants will grow to give us backyard privacy?

First what is your hardiness zone?

This Hometalk had a similar question, I think her answers will help you out! https//www.hometalk.com/diy/outdoor/garden/q-planning-for-summer-how-to-add-privacy-accross-back-treeline-12315795

And, there's a lot of fence options if you want something that doesn't need the same kind of maintenence http://www.hometalk.com/diy/reclaim-your-backyard-with-a-privacy-fence-3621848

bamboo!

Remember anything that grows fast and large will a maintenance nightmare if a few years . I believe that some type of screening device is a better option and is immediate. Try a sun sail, curtains, lattice screen or a tall wire trellis to grow vines on. My neighbor planted arborvitaes between our yards, not only do they have to maintain them, because the split and fall in the winter. The roots are voracious . I need a jack hammer to plant anything 5 feet from them.

Great suggestions so far, I love bamboo but plant them in their pots sunk into the ground, that way you will have privacy, easy to maintain, sound reduction, able to enjoy the breeze also. You can combine these with a trellis or similar with climbing plants for colour and scent.

Bamboo is the best quick screen just be sure to plant it correctly. It's invasive. There's a website, "Fast Growing Trees"

which might give you other ideas. I'm a big fan of climbing plants which soften a privacy fence. You could plant climbing roses, trumpet vine, honeysuckle etc., and plant annual climbers to fill in until those are established...scarlet runner bean, sweet potato vine, ivy, etc will do the job.

Many types of cypress trees grow tall and quickly. Check with your local garden center (not a box store one) and they can tell you the best types. Many grow 5+ feet in a single year. I have the same problem since my new neighbor cut down all the trees between our yards and I'm planting Carolina cypress trees next month to start shielding me from view.

Forsythia. complete wall in a couple years.

i did this in an afternoon with 30 days of growth, $40 for the deer fencing and $5. For seed

At the end of the season..I mow around and compost the vines.