Any plant grown in a flat plane is called an "espalier." To maintain this shape requires a lot of pruning, and a fence, trellis, or wall to grow against, but it is useful in the urban food-growing context because fruit trees can be grown in an extremely small space.
Although I have never seen this done (nor yet found anything on the internet about it) it occurred to me that chain-link fence is an ideal support medium for espaliers. I live in Roslindale, a neighborhood of Boston, which I had dubbed "the land of the chain-link fence." When I discovered the espalier technique in my handy Rodale's Encyclopedia of Organic Gardening, a light bulb went off! The main expense and trouble with the espalier technique (to my mind) is stringing the wires for support across a suitable surface. A chain-link fence is already in place and very sturdy. A bit of research shows that it is the ideal height for a single or double horizontal (see Figure 1. in the University of Florida Extension Circular CIR627 - http://edis.ifas.ufl.edu/mg273).
I measured my fence, which seems standard, and the top rail is about 3.5 feet - ideal for the second tier - the first tier would fit easily at 2 feet and could be tied to the lattice-work wires.
More later on which plants to buy....
M-m-m-mh, apples, I think.