Along the same lines as the "running without A/C" post, I looked around for information on whether a dehumidifier would save me money since dry air feels much cooler than hot air (as with Houston versus Arizona).
Sadly, the answer looks like a big no. Dehumidifiers are not energy saving, only energy efficient. This means that one costs less at the end of the day and the other merely costs less than other similar devices. In other words, you should only purchase one if your house is unusually humid, having a noticable problem with mold, or if you have bad allergies. If from allergies, you should probably rent one first to see if its useful. Dehumidifiers help reduce dust mites, which you might not be allergic to.
Dehumidifiers are not energy efficent because the device works as both a cooler and a heater. It cools air so that water condenses and then heats it again to get it to drip into a container or down a tube and into a nearby drain. This process uses more electricity than your existing air conditioning system, which (as I understand it) only needs to cool the air and uses the warm air outside to draw the water away.
So ... hope that helps someone.