Bcarroll:
I got a little further. I hacked up an old ATX power supply and tried using the 5v line from one of the molex connectors. I can get the left arm to move (shoulderX, shoulderY, elbow, wrist), but none of the others respond. I think I will try the 5v line from the motherboard connector. I think I read the molex connector has 5 amps, but the motherboard connector has much more available.
That sounds like a good next step. As zoomkat mentioned, and unlike many other projects, the servos must act as an integral part of the physical structure. It isn't unusual for each small servos to draw between 1 A to 2 A when most of them are supporting the weight of themselves and/or other servos. So you'll want your power supply to provide a maximum about 2 A per servo, just to avoid the possibility of starvation if the majority of them are moving at the same time. Depending on exactly how much current the 5 VDC line to the motherboard can supply, you may have to use the 5 VDC on the peripheral power cables (you called them molex connectors) for a couple of the servos.
Another thing to keep in mind is because of the way current divides in parallel, you could tie all your 5 VDC from the peripheral power cables together and the current draw would be distrubuted approximately equally through each of the cables. If you are planning to have the power return to PSU via those cables, remember to do this with the grounds as well. For example, if you have four peripheral power cables you could have a total current of 18 A to the servos without drawing excessive current through any individual cable.