The Fire TV Stick’s product page clearly says “Fire TV Stick cannot be powered directly by your HDTV”. However, while perusing through the recently published Fire TV Stick User Guide, I’ve found the following:
You can plug your Fire TV Stick into your TV’s USB port
for power, but using the supplied power adapter is
recommended. Some TVs have a USB port, but it might
not provide enough power.– Fire TV Stick User Guide
So it seems, while not recommended, it is possible to power the Fire TV Stick via a USB port if the port produces enough juice. This is good news for those wanting to take full advantage of the device’s tiny footprint by reducing cable clutter.