Thinking through the principles of wall gardens this morning... while some types of wall gardens have existed for thousands of years, the idea of the wall garden as it's described here evolved from a series of highly evocative drawings by Julie Sanford, who is an extraordinary New Urban Guild architect and who is Town Founder of Sky in the Florida panhandle. Sky is a DPZ design.
Plants are smallest at the point they enter the ground... this much is obvious. So long as the roots have room to spread and the earth has the right mix of moisture, nutrients, etc., you don't need a large area of soil where the plant is planted. Look at street trees all over the world, planted in a small tree well. Today, of course, the urban foresters will tell you that "the tree isn't happy unless it's planted in a planter that is at least (100, 200, 500, 1,000... depending on which urban forester you're speaking with) square feet." But countless street trees planted before urban forestry emerged as a discipline tell a different story.
The ancient practice of espaliering fruit trees against a wall should be expanded into an entire branch of gardening that could be called "wall gardening." Wall gardens make lots of sense because the physical limitation of a garden isn't the square footage of the soil where the trunks enter the soil, but rather how far the plant can spread as its leaves seek sunlight. So training plants up a wall uses a surface area (the wall) that is a lot more plentiful in urban areas than the normal garden surface (the ground.)
All fruits and several vegetables are candidates. Fruit trees work well because you only have to train them occasionally, and once a branch is properly trained, it stays there for the remainder of the life of the tree. Fruit bushes work almost as well, for similar reasons.
What about vegetables? Most vegetables are annuals, so they must be trained in their entirety each year. This can be a lot of work, depending on the plant. Vegetables that vine naturally, such as beans and peas, work much better because you can simply point them in the right direction and they do the rest of the work themselves, including attaching themselves to the framework with tendrils.
Some vining vegetables, however, don't work because the fruit is too heavy. Can you imagine watermelons growing on the wall of your house? ... actually, I just tried to imagine that, and my mind couldn't process the image, so it created a solution to prevent mental meltdown: Imagine heavier stuff like melons and squash vining up a wall. Now, imagine little wire baskets that the urban gardener would hang from the framework wherever a melon or squash sets on the vine, so that it can mature in its own little cradle. Once the fruit is harvested, the cradle, which simply hooks over the framework, can quickly be taken down. So if you do that, then anything that vines could potentially be used in a wall garden.
There are other vegetables that don't precisely vine, but that lend themselves to easy instruction as to where to grow. The tomato is an obvious candidate; everyone has seen tomato cages used by gardeners everywhere.
So where do these wall gardens occur? Think of the factors involved: you need to be able to reach the wall, so that you can tend and harvest your bounty. So the wall needs to be within reach, either standing on the ground or on a fairly low stepladder. In other words, don't garden so high that you get yourself killed if you fall. So this limits the garden to the first-floor walls of your house or shop, or to upper-level walls at a porch or gallery if you're doing container gardening there.
There's also the issue of plant height. Beans might run a full story during a growing season, but many vegetables won't get much more than half the height of the wall. So maybe you should consider a two-tier garden, where the annuals run up to the bottom of the windows or somewhere similar, and the espaliered fruit trees are trained to the wall above... just a thought.
Also, think about orientation. A western wall in some climates might fry certain vegetables; maybe you just do espaliered fruit there, and with some shade from adjacent trees planted conventionally. And northern walls that don't get direct sunlight need to be carefully thought out; not everything will grow there.
One more issue: your wall material. Each material has its own set of issues, but the one I worry the most about is wood. This is because a heavy load of plant material can hold a lot of moisture against the wall, which is generally a bad idea with materials that rot. So the wall garden might not work everywhere. But today, most siding isn't wood, but is instead cementitious, like Hardi-Plank. So just make sure that a wall garden makes sense for your particular set of conditions.