If this happens as soon as you plug in a usb device, then its most probably the port shorting out. It does tend to happen sometimes, but rarely is this a software or power issue.
Hopefully your case is an aftermarket model. If so, you can start by removing the usb ports from the front (hopefully they're screwed in and not glued on). Keep the header plugged into the motherboard, but have it detached from the case. Holding it in your hand (or just not touching anything metallic), power on your computer and plug in a usb device. If it still powers off, then there's probably something wrong with the ports themselves. If it stays on, then its definitely a short.
If you conclude that its a short, power off your computer and reassemble the usb header onto the case. Just make sure that nothing metallic is touching the usb port itself. If you can't isolate it, try covering it in a piece of paper before screwing it back on.