As of this writing, most of the affected servers are still down. Blizzard is aware of the issue and is looking into it, but has no further information to give at this time. We'll update this post when we hear more.
UPDATE: According to Crygil, tonight's issue was out of Blizzard's control, but luckily things have resolved themselves. All realms should be up within the next half hour.
[Thanks to everyone who gave us a heads up!]
UPDATE: The 8 PM Pacific ETA has been removed from the original notice. This could be a long night.
UPDATE: 8 PM Pacific time is the current ETA for the return of the affected servers.