USB hard drives (version 1.x and 2.x) cannot be powered by the USB bus – there isn’t enough power pushed down the cable. You must use the device’s A/C adapter.
In contrast, many FireWire hard drives can be used without an A/C adapter because the FireWire specification includes sending power down the cable. This is handy for making backups, storing your iTunes library, etc. but I’d stick with A/C powered drives for video editing or any other serious work.