I haven't grown them yet, but just bought seeds for Bitter Melon and Malabar Spinach.
And there's always pole beans.

Bitter melon vines will easily train up a fence but malabar spinach needs to be secured. The bitter melons are really pretty when you let them over-ripen on the vine. They'll turn yellow and split revealing bright orangy red covered seeds. You could also try passiflora vines. Edulis produces a nice fruit and some are self pollinating. Not sure which. You can check on the passiflora forum. Red Noodle beans are an interesting choice. The flowers are pretty as is the pod and it does quite well in the heat.

Scarlett runner beans have beautiful flowers as well as good beans.

Would you consider coming out a little bit from the wall with an arbor or two/few? I find this sketch of Van Gogh's inspiring - http://www.the-athenaeum.org/art/full.php?ID=25669 - maybe wider than long or perhaps in a corner? Kiwi and grape vines might be easier that way than trained flat against a wall.

Karyn's idea about noodle beans is excellent. I don't know if this is true only in my garden, but I find that those pesky Mexican bean beetles don't go near my noodle bean vines, whereas they are horrible on regular bean plants.

It might make an interesting experiment to see what would happen, if you were to drop string from an arbor down to pots of tomatoes - they can be trained to a single trunk. They might climb up string more naturally than something thicker. Or, maybe drop down a length of trellis, perhaps made from twine or nylon - then summer squash, cucumbers and unpruned tomatoes could join the party. Planting them in pots like this would bring them out from the wall, where with better air circulation, there might be less problems with powdery mildew and other leaf diseases.

For me, the noodle bean vines are very easy climbing up string, but not something thicker.

If you try the foregoing idea with vegies in pots, following are some do-it-yourself instructions for making self-watering ones -

http://www.josho.com/gardening.htm
http://www.seattleoil.com/Flyers/Earthbox.pdf
not sure about this one: http://www.hgic.umd.edu/_media/documents/HG600Containerveggardening.pdf
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If you do find yourself taking breaks or watching sunsets from your arbor(s), I personally could not refrain from letting a vine or few travel up string that would attract hummingbirds - there are many - but my favorite is Ipomoea sloteri (syn I. multifida)...or moonvines for hummingbird moths? A red Scarlet O'Hara morning glory with red going all the way into its throat would be gorgeous.

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Perhaps not efficient time-wise, but espaliering a quince against a wall could give you flowers in late winter...not to mention an apricot, Prunus mume and its fragrance.

Hope I said something useful,
Karen

I also bought bitter melon seeds and will give them a try this summer. I want to make a living curtain to shade a window from afternoon sun.

I would enjoy hearing how you prepare the melon to minimize the bitterness. I read online you must remove the whitish colored internal material before using the melon in a recipe.

Joseph

Ipomoea aquatica (Chinese Water Spinach) - http://en.wikipedia.org/wiki/Ipomoea_aquatica

I grew this one in a pot that was sunk into a tiny muffin "pond" liner filled with water and other aquatics, and it did very well - give this one a sturdy, ample trellis. Can be extremely invasive.

There are several highly ornamental Dioscorea species that produce beautiful vines and edible tubers that are a staple food in many parts of the world. Some of them also produce edible bulbils that can be removed and prepared as food. Avoid the one known as air potato (Dioscorea bulbifera) because it requires too much preparation to remove the bitter taste from the tubers and above ground "potatoes" in order to be palatable. D. alata, D. oppositifolia, D. rotundata, and D. japonica are a few of the commonly eaten and easily prepared species. Before any of the Miss Grundys out there start screaming about invasiveness, please note the topic starter doesn't live in the tropics or the Deep South.

"Strawberry Pouches" - http://www.rnzih.org.nz/pages/Growing-strawberries.htm

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Another technique in gardening on vertical walls involves rockwool as the growing medium. In the search box of www.google.com type in "vertical gardening" + rockwool

The National Arboretum in Washington, DC once made a garden of many rooms out of rockwool cubed modules linked with trellises and arbors. The walls of flowers and vegies and vine-festooned arches turned that garden into a magical fantasy.