There don't seem to be a lot of specifics in this thread and I've noticed a lot of people asking questions that could all be answered quickly. This is a great thread, but I feel a few more details would help tremendously.
When you have a PC fan it should say on it the volts it is designed to run at and the amps that it pulls while running at full speed. If you have a 12vdc fan that pulls .38Amps you need a DC power adapter that can push the same or more amperage. On the power adapter it will say the current output. I have a 12vdc power adapter with an 800ma current output, and because both of my fans pull only .38A (or 380ma) each, it powers them both just fine. If you are pulling more amps than the power adapter is rated for, it will eventually burn out which can be a fire hazard. If you have 3 times as many amps as you need, that's fine. The fans only pull what they need, you cannot over power them unless you're using a higher voltage.
Which leads me to my next topic. Two things can happen when you run a fan at a different voltage than it's designed for. If you run it at a higher voltage, like the power supply, it will eventually burn out. If you run it at a lower voltage it puts strain on the motor and will lessen the life of the fan.
Batteries naturally output a DC current, so you can power anything that requires DC current off a battery, as long as the battery can handle the load.
Hope that helps some people =)