Very good point Sylvia.
I know many people have struggled over the past several years trying to come up with some means of doing aquaponics without electricity. There might be some ways to do it, however, so far what I've seen has been rather impractical and since most people trying to do it that way don't want to spend a lot of money up front on windmills, so far I've not seen one get built.
It might be possible to build a system where one could go out and hand pump (pedal pump etc) or bucket water up to a header tank several times a day and let that water trickle through a system but the header tank would need to be huge and the fish load in such a system exceedingly small to the point of not really making sense unless one just really liked to build things and get their daily work out moving water.
Anyway, these things could be possible but generally very impractical for the average back yard. Some work has to get done some how to lift water and if that work doesn't come from electricity, time to start looking up other means of pumping. Windmills, rope pumps, ram pumps etc but don't expect a perpetual motion machine as there are always efficiency losses so it isn't like you can start off a bell siphon in one container and expect it to kick off a bell siphon in another container to lift water back to the first container, that isn't going to work well since the water exiting the siphon always needs to be lower that the start point.
Not to stick out like a sore thumb, but if you really really want to limit your footprint go vegan :) or raise your own cattle.
1lb of beef takes 2,500 gallons to grow http://www.vegsource.com/articles/pimentel_water.htm
Carbon footprint savings for going vegetarian / vegan http://planetgreen.discovery.com/food-health/vegetarian-diet-carbon...
While I am bias I am not vegan to reduce my footprint, it is just a side effect, I am vegan to eat healthy based on my years of studying nutrition.
Replacing one incandescent bulb with a LED light bulb prevents the release of 300 pounds of carbon dioxide in just one year. http://www.squidoo.com/incandescent-versus-CFL-versus-LED
If your end goal is to be off the grid then I would start looking into batteries because they are what cost the most normally in the system.
You could find a creek in your property and make a water mill to power the movement of water in your system :)
Most of these things are outside the realm of most peoples budgets however (solar, wind, hydro etc)
As far as I know there is no way to move water uphill other than an electric pump. An aeration pump or blower typically uses much more energy than a water pump. To really off set your energy consumption find a way to aerate your water without a blower. For example you could build in a waterfall falling into your fish tank/pond.
Water can be lifted without electrical power. It takes something mechanical like a manual pump (hand pump, rope pump) or windmill or there are ways to use other moving water like a creek or waterfall near by to lift water by turning a water wheel or tube pump or operating one of the other manual pumps or there is something called a ram pump but I don't know if that would work because it pumps part of the falling water back up higher instead of pumping the system water.
Most of the mechanical means of pumping water are either too labor intensive for out "western society" or require features that most backyards don't have access to (like the natural creek or water fall or good space for a windmill pump.)