なまず 速報 β Recieves earthquake push notifications
Misc: Don't change default keep alive settings.
Features: Wake on notification; cancel silent mode on push; restrict notifications by richter magnitude, Japanese "shindo-scale," and/or distance from epicenter
The Dev warns that this app is very experimental, so your milage may vary. It worked but killed my battery because it appeared to open a sustained connection to an external server and prevented the phone from sleeping.
Based on this comment by Yin Lung Lee and the app's excellent rating, I recommend downloading it and giving it a try.
Using Spare Parts, go to Battery history and select "Other usage" and "Since last unplugged." Clicking "Running" will tell you how long your phone has not slept. If you have the same issue as I did, to uninstall, you may need to go Settings/Applications/Running services and kill it first.
東京電力供給情報ウィジェット TEPCO Power Supply Widget
Misc: Not an official TEPCO app
Features: Uses the TEPCO power supply API
I saw this come across the @OffcialTEPCO the other day. It gives a pretty good idea if there will be a need for major blackouts that day by showing a comparison to the current usage relative to the previous day's usage, as well as the total capacity.
As far as apps for searching which areas are scheduled for blackouts, there are a bunch, but I haven't found any of them particularly useful. Much of this is likely due to TEPCO's scheduling. (This is why I've been using the above widget.) Here are a few of the more popular ones on the market:
Pro: Uses GPS
Con: Has permission to make phone calls (for calling TEPCOs blackout info center according to the dev), which I personally don't like.
Pro: Has no scary permissions
Con: Has no special permissions at all - no GPS.
Developer: Isana.net inc.
Pro: Uses GPS
Con: Don't know. New app. Haven't used it.