The problems seem to be originating from people who have not yet merged their World of Warcraft accounts with their Battle.net accounts. To do so, go into the account management page and select the appropriate options.
There have been some stability issues with the login servers the last few days, and this seems to just be the latest.
If you can't get in, check out our Guide to Patch 3.2 - we're expecting the patch to drop within the next few weeks. And if you haven't heard already, the Warcraft Movie has landed a director - Sam Raimi. It's World of Spidercraft, baby.
Update: Now there is an official Blizzard response to the problem, although there is no ETA on a solution.
Update #2: For those wondering, the issue was fixed overnight.