i've dabbled in some low-tech hydroponics, and am somewhat familiar with different systems. From what I've found online about the Aerogarden, it sounds like a modified drip hydroponics system where nutrients are released over the plant roots and drip down into an enclosed reservoir. The reservoir is not full so the roots are hanging down into an open area with 100% humidity. The combination of optimum nutrients and oxygen exposure make for excellent growing conditions. (Little nitpick: one slightly misleading thing about the aerogarden is the "aero" part of the name; it implies a technique called aeroponics where nutrients are sprayed directly on the roots. But that's just a technical difference in nutrient delivery. In terms of maintenance, the drip system is easier to handle.)
One word of caution.... if you have a power failure lasting several hours, the root environment could get pretty dry so it's important to keep the roots hydrated by manually pouring some nutrients from the top every now and then.
I've not used this system but the reviews I found at
http://www.chowhound.com/topics/383547 were generally positive. It sounds pretty fool-proof but that doesn't mean the system should be ignored. Like any hydroponics system, expect the plumbing to occasionally get clogged or partially-clogged, but if the tubing and pump are accessible, it should not be too difficult to clean.
If I had the time to play, I'd get it. It sounds like fun. I don't know if it will ever pay for itself, but if you're looking for a neat toy, go for it!
If money is an issue, you could probably cobble together a home system ... it may not be as efficient as the aerogrow and requires more attention, but the results will be pretty good. A few years ago, I put together a simple show-and-tell webpage for family and friends.
http://home.comcast.net/~whimbrel/hydro_img/hydroponics.html -- if you scroll to the bottom of the page, you'll see a home system I put together using a rubbermaid tub, air pumps, aquarium airstones, and clay balls. I got pretty good results from that system, but never had time to photograph the results and post them on the page. But if I had to do it again, I'd skip the clay balls and build a styrofoam raft with holes to seat the pots. That would cut down evaporation, making it easier to control nutrient concentration and there would be no annoying sound from clay balls being knocked around by the air bubbles.
A note about lighting ... the fixtures in the photos are easily available from hardware stores like Home Depot. You can get bright fluorescent light bulbs that mimic the solar spectrum from hydroponic stores, ones that will fit regular light bulb sockets (I cheated ... regular warm white spiral fluorescents worked fine). If you're growing more light-hungry plants you'll need compact fluorescent systems which are more expensive, and for plants like tomatoes, metal halide systems that are super-bright and super-expensive. Check out the hydroponic online stores (just google hydroponics) to check out the many growing choices out there. It's loads of fun!