I had a look at an Aquaponics and though I quite liked the system there where some things I didn't like about it such as the energy consumption of the pumps and that amount of fish in a small amount of water can cause problems with all the fish dyeing.
edit 26/7/12 Just a note on growing root vegetables. A number of readers have pointed out that some people have successfully grown root crops in both a hydroponic and aquaponic systems. I have also spoken to "experts" who have told me no way, there are problems with crops going rotten. http://www.instructables.com/id/Hydroponic-Food-Factory/step17/Hydroponic-potatoes/ give a short description on how to grow potatoes in a hydroponic system.
I'm not able to grow a traditional garden, as we have extremely poor soil, water restrictions, low rain fall, and extreme weather events such as week long heat waves of 45C or 113F which will kill any veggie within hours.
I started this project about a year ago and at the time it was an experiment to try an address the above issues, I had never heard of vermiponics, and there is still not a great deal of info about it. It wasn't until a few weeks ago I found that it had a name and there are some similar systems out there. Stupidly I didn't take a lot of photos and it is now July and the middle of winter so the garden doesn't look that good at the moment. I will up date photos every month for the next year or so.
Step 1: How it works
The bottom tanks are joined together with poly pipe and a solar pump, pumps water to the top storage tank. The top storage tank has a siphon inside it and that trips off around every half hour in full sun, which waters the plants. The plants are grown in soil and taste fantastic (no sad watery acid hydroponic tomatoes here)
The soil in this area is very poor and aqua-phobic ( will not absorb water) so I use a mixture of soil, animal manure, lawn clippings, leaves, food scraps,wood ash and a box of worms to get it started. The worms have gone mad and turned the soil in to rich dark loam and the plants have thrived.
Below the soil is several layers of shade cloth to keep the soil out of the layer of gravel which is at the bottom of the top tank and to provide drainage and a home for microbes. The water then drains into the bottom tank and the process starts again.
I had a problem with mosquitoes in the bottom tanks when first set up, a couple of gold fish in each tank soon fixed that.
Another problem when first set up before the worms became established was the soils poor nutrient level as the plants were not growing very well, some organic liquid fertilizer helped in those first few months
As the worms started working the water became so full of nutrients that it became possible to grow leafy greens in a gravel bed.
Here is my first crop of lettuces grown in gravel.