We'll keep this post updated and time-stamped with the latest news. You'll only need to look here to know.
6:45 p.m. EST: There is still no ETA on the fix. Downtime will continue for the time being. Another update will be provided in an hour. In addition to the game being down, the forums are down, the Blizzard store appears to be having issues, and the official Warcraft website is loading extremely slow. WoW.com is handling the excess traffic fine, thankfully, so we should be able to continue to provide you with any updates we get.
7:05 p.m. EST: We are getting reports that some realms are up. Your mileage may vary.
Older updates are after the break.