I had seen one ATX based computer, that had the ability to power on itself, when another computer RINGS on it. I don't remember the exact model and type.
Added after 29 seconds:
There are few more advanced feature in ATX power supply.
They remain on to supply the 5 V-standby voltage to USB ports (if enabled).
But that is just for convenience - you can turn it totally off with the switch in the back.