We did some experiments with the Kinect after we split open it's power cable. We hooked up the positive end to a variable power supply and the negative end to ground. We found that at 12V the Kinect operates and draws about 0.35A. We kept decreasing the voltage and we found that the minimum operating voltage for the Kinect is about 8.5V. At this level it drew about 0.42A. For all you Kinect hackers, the Kinect operates at under 9V!
If you want to power your Kinect wirelessly, just hook it up directly to 8 AA batteries and it will work just fine. The amount of time you get out of the AAs will vary with your use, but don't expect something in the hours range.