Michelle, what direction do these walls face, and what kind of sun do they get?

I'm embarrassed, but I'm not positive how to answer the question of direction. If I'm standing on my back patio looking at the wall it is south. If standing with my back against the wall and looking at my house it's north. So I guess it gets hit with light from the north?

It gets lots of direct sunlight, but does have periods during the day with minimal shade.

I think there are many plants that would work, including shrubs and vines. Are you partial to any plant in particular? Do you just want privacy or would you like blooms as well? And do you know the neighbor behind you? I ask because a lot of what you could plant might (actually, most assuredly will) grow through the openings and onto the neighbors side of the fence. Sadly, there have been many accounts of feuds started just over that issue. If you know the people, you might have a conversation and come up with something you both like. For the life of me, I can't fathom why someone would build a fence like this in the first place. So... can you provide a few more clues? I'm guessing you want an evergreen vs a plant that drops its leaves in winter?

Nice diagram, thanks for including it! If it was mine, I'd use my go-to plant for privacy, hopseed, or "hopseed bush" or "hop bush" (Dodonaea viscosa). It tolerates any light except black shade and is non-toxic which is nice (I'm an oleander fan but it is toxic).

I would probably plant it the whole length of the fence to create unity, but if you just wanted to use it for the privacy part, and then maybe repeat it a couple of times along the rest of the fence, and then fill in in-between with other fun plants, that would be nice too.

I would also make absolutely sure to keep the back side/neighbor side trimmed too so that it doesn't poke through the openings onto their side. I know it seems odd to trim their side, but if you plant it a bit away from the wall/fence you'll be able to keep the back side trimmed so it doesn't reach out into the neighbor's garden. Just seems like a good neighborly practice to me, and one that I do as well.

I'm sure you'll get lots of other great suggestions too. Let us know what you select and how it works out!

Take care,
Grant

Here is a link that might be useful: Hopseed bush on Desert Tropicals website (growing plants in Phoenix)

The tips about keeping it trimmed for the neighbors and asking them about it are good ones. I had wondered about speaking with them, but didn't know if I was being overly worried or silly. I will definitely do it now!

Tomatofreak: Yes, it is a very strange set up. Everyone that visits wonders about that fence. We would prefer something that blooms, but it isn't a deal breaker. An evergreen definitely sounds like something we'd prefer to not have to deal with the leaves dropping in the winter.

Grant_in_arizona: Thanks for the link. I do like that. Do you plant the red or green?

Michelle, I - like Grant - was a big fan of hopseed. Not any more. I planted the so-called red which, as it turns out, is only 'red' in winter and green the rest of the year. Of the 6 that I planted along a chain link fence (for privacy), there are none now; they all died. So have most of the ones my neighbor planted on a berm in their front yard.

I planted duranta, Sweet Memory,along an east-facing block wall, never expecting it to grow so big. I have six plants that pretty much cover a 50' stretch of wall and tower above it. It is evergreen, has beautiful lavender/purple blooms and makes berries that birds eat. http://patwelsh.com/wpmu/blog/pruning/duranta-sweet-memories-pruning/

There are many more plants that would work, but finding out what the neighbors think, like, want or don't want should come first. If worst comes to worst, you can always fill in the spot by attaching hard material to the uprights and plant whatever you like on your side.

Green timber bamboo

Seriously? http://bamboodirect.com/bamboo/catalog/timberctlg.html

I prefer the green over the purple hopseed, atlhough I accidentally added one purple to my "hedge". I kept them on drip irrigation their first two years and now they just get watered from my hose when I think about it. Tomato, I wonder what happened to yours?? Egads, that would be bad news if mine croaked too.

Let us know what you select and how it works out! Happy gardening!

Grant, mine were on a metered drip system, too. I'd notice leaves starting to dry and brown and before long, a whole branch would be dry and brittle. They just seemed suicidal. Same thing is happening to my neighbor's, too. Oddly, they're advertised as drought tolerant, so you'd think they wouldn't need much water.

Huh, that's too bad tomato. I wonder if they got TOO much water?? You see them growing wild just east of the Valley (especially around Globe-Miami etc) and they seem happy? I have no idea though. I'm going to completely remove mine from any and all irrigation this spring/summer since I'm tired of hacking them back anyway, now, LOL. Happy gardening all!

Another thing I discovered about hopseed: There are male and female plants and they grow differently. At this point, if I wanted a raggedy-looking plant that was drought tolerant, I'd plant creosote. At least it would smell nice when it rains. Well... when I spray it; I don't think it's ever going to rain again. :(

From what I have read, hopbush is a short-lived shrub. It grows fast so would be a good temporary hedge to cover until a more permanent type of plant could grow up enough to take its place.

Have you considered jojoba?