The world server is apparently going up and down, and many servers are experiencing connectivity issues. Blizzard lists the realms that are not working well at the start up screen. But as I'm finding out over on Anvilmar, the problem has spread there too.
According Isradun, multiple realms are being restarted now. There are additional posts on the WoW Realm Status forums that indicate they've already been at this for a while. However, as I've tested, no fix appears to be working perfectly yet.
We'll keep this post updated for you with the latest.
Update, 12:05 a.m. EST: Apparently the realm issues are subsiding, although no Blizzard update yet. Some reports are still trickling in of issues in the Nightfall and Reckoning battlegroups.
Update, 12:18 a.m. EST: Blizzard saw what I said and decided to start crashing realms again. Multiple Tech Support Forum posts report things are not well, again.
Update, 1:08 a.m. EST: Everything appears to be working now. Blizzard has removed the opening announcement, and the spam on the forums has quited down. Enjoy the night!