Updated: Blizzard has informed its community that they are currently working on a fix to the server issue.
Below is their official statement:
We are in the process of performing an emergency maintenance for all North American Diablo III servers to resolve several issues that are currently impacting the game. This maintenance may cause some interruption in communication, ability to log in, use of in-game features, and disconnections. We anticipate all servers will be available for play in approximately 1 hour.
Thank you for your patience.
Original: While one lucky gamer already beat Diablo III on its first day of release, others are having trouble just playing the game.
According to Diablo III Community Management there are several errors that appear when players attempt to login to the game.
Here are some of the errors that have been reported as of this morning, If you are receiving these errors read on to see what you can do:
We’re aware that some players are experiencing Error 37 when attempting to log in to Diablo III. This error indicates that the Diablo III server is full and is likely the result of high login traffic. If you receive this error message, please wait and try again.
Error 3005 and 3006
Along with Error 37, we’re also aware of players receiving Error 3005 and Error 3006. If you receive either of these messages while playing, please wait and try again.
We’re still looking into these issues; however, a player workaround is available. If you are experiencing either of these issues and are using Windows, create a new user account with administration powers (http://www.wintuts.com/Manage-User-Accounts). From there, log into Diablo III.