If you're one of the people who tried to play this past Tuesday, you experienced the same thing as the rest of us. The servers, they were just plain dead. Even since then, the instances and world servers have been a little less than friendly. This was all to put in Patch 3.1, but there were definitely some hiccups along the way. The game just hasn't been running smoothly, and some folks haven't been able to play at all.
Bornakk dropped by the forums to tell us that they plan on doing something about it. All World of Warcraft accounts in good standing will get one day's free play time. Your account has to be based in the North American, Latin American, or Oceanic servers, but it will definitely show up in your Account Management login within the next few days. Totally classy move on Blizzard's part, in my opinion.
EDIT: EU and Russian servers, too!