Sounds like a north facing wall. I planted a cactus garden two years ago, it's doing well.

do you want something that's evergreen throughout the year?

Are you thinking of shrubs? If so, I've noticed the Ilex Vomitoria (Dwarf Stokes) seem to do ok under these exact conditions. And they're quite pretty...although they do grow quite slowly on my north side.
I'd also recommend African Boxwoods; mine do pretty well except for the fact that I accidentally over-watered one last year, so it died. I think the key thing is checking the soil and refraining from watering when it cools off.

Both are pretty frost hardy...never had to cover either during winter(I live downtown).

Yellow broom is another good shrub that likes the sun and it's frost hardy as well.

Hawthorne,ruella, phoenix robellini,roses,citrus trees, ice plant...... really just about anything that likes the hot summer sun should work. Just cut way back on the water in the winter.

Thank you all for you suggestions. I just moved here from last September after spending my whole life in the Northwest. This year has been a challenging year and huge learning curve for me. Most of my 'full sun' plants died in the summer heat, I watered my cactus way too much, and my palms all look like crap. I am geared up and ready for year two, haha.

Welcome to gardening in AZ and to this forum. We hope you'll post a lot, and often. :) I moved here from Seattle in 2000 and absolutely love it here, gardening included.

You've gotten some great suggestions for sure, so let us know what you select and how it works out. My north facing walls get sun in summer and shade in winter. I've had great luck with red "yucca", Hesperaloe parviflora, good ol' Aloe vera, and African "ocotillo" (not at all related to our native ocotillo, but it does look sort of similar), Alluadia procera. Good luck and let us know who the lucky winner is and how it does.

There are some great local gardening books that are great resources, along with this forum of course. :) Post often!

Take care,
Grant

Here is a link that might be useful: My garden pics October 2011

I have the same kind of spot on the north side of my house too. I put an herb garden in. Things like basil, rosemary, oregano, thyme and even mint survived full, strong sun all summer. It's doing well in spite of having no sun at all since back in September (although it'll die off when frost hits of course).

Other plants I have on that side that are doing well include yucca, katie ruellia, bougainvillea, emu bushes and palo brea trees. Very, very little water in the winter and plenty of infrequent but deep watering during the summer keeps everything strong and healthy. I've been in the desert for 8 years, gardening the first year was a total disaster...you'll learn :)