I've been interested in hydroponics for quite some time. It's part of a growing interest that I have in sustainable and decentralized production of food and energy. At the Maker's Faire, there was a display of a system which integrated both hydroponics and aquaculture: fish were grown in a tank, whose water circulated back to water some plants. This is called "aquaponics". Digging around on the Internet this evening (hey, I was bored) yielded this excellent manual on a beginning system that uses a series of barrels. It seems very practical, and answers many interesting questions. The total amount of food produced is quite small, but the overall system is quite interesting. I'll have to print it out and read up.
Addendum: Here's a little Youtube video detailing a system built by an amateur. It uses goldfish and carp fingerlings, and he is growing tomatoes and other vegetables and flowers.