According to Drysc, there's a Blizzard-external network problem in the central United States that is currently affecting several WoW realms. Symptoms include high latency, packet loss, disconnection, or inability to connect; side effects may include broken keyboards and bruised fists, or in severe cases, deciding to stop playing WoW for the evening.
I'm not sure which realms are affected, but it's nice to know that this is being worked on anyway; the glowing tree promises that they are actively receiving updates from the (unnamed) parties involved. There is currently no ETA on a fix. I'll keep you posted if I hear anything else. In the mean time, let's start building a list: if your realm is acting up, let us know in the comments.
Update: Drysc is saying the issue "appears to have been resolved," but they're still keeping an eye on it.