(UPDATE-4) As of 2:20PM on March 19, 2013, cooling of Reactor 1's Spent Fuel Pool resumed. No information about other SFPs and facilities affected by the power outage.
(UPDATE-3) The temperature of Reactor 4's SFP is 30 degrees Celsius, up 5 degrees since the power outage.
(UPDATE-2) More than 15 hours after the power outage (Japan Time 10:30AM on March 19), there is still no power. TEPCO is having a press conference right now. The new spokesman who croaks is not very good at explaining things in a straight-forward way. (My guess is that he doesn't know well what he is talking about, unlike his predecessor Matsumoto.)
In June 2012, cooling of the Reactor 4 SFP stopped for about 30 hours when the pump of the secondary cooling system burned out.
(UPDATE) Jiji Tsushin says the water temperature of Reactor 4's Spent Fuel Pool (the "hottest") is about 25 degrees Celsius. The safety standard for the SFP temperature is 65 degrees Celsius, and it is estimated it will take about 4 days without power to reach that temperature. In the Reactor 4 SFP, both used and new fuel assemblies are under 7 meters (23 feet) of water. Fuel assemblies are 4-meter (13 feet) long. According to the plant operator (announcement from May 2012, in Japanese only), it takes about 3 weeks for the water 5 meter deep (i.e. still leaving 2 meters of water above the fuel assemblies) to evaporate.
The common pool has old fuel assemblies whose decay heat is already very low.
It took three hours for TEPCO to announce the power outage at Fukushima I Nuclear Power Plant. (Same old, same old...)
From Kyodo News (3/19/2013):
Power outage at Fukushima I Nuke Plant, cooling of spent fuel pools stopped
TEPCO announced on March 18 that there was a power outage at Fukushima I Nuclear Power Plant slightly before 7PM. Cooling systems for the spent fuel pools in Reactors 1, 3, 4 has stopped, and as of 12:25AM on March 19 there is no knowing when the systems will be back. Power went out also in Anti-Seismic Building temporarily but it came back on quickly.
According to the Nuclear Regulatory Agency, there is no problem in injecting water into the reactors. Cooling of the common spent fuel pool, which contains 6,377 fuel assemblies, has also stopped.
According to TEPCO, the problem could be either the switchboard or the cables connected to the switchboard. Both the Nuclear Regulatory Agency and TEPCO have been unable to identify the cause. TEPCO announced the power outage after 10PM, three hours after it had taken place.
The plant receives its electricity from Tohoku Electric Power Company. There is no problem receiving this external power.
(H/T reader Beppe)