It seems as if the Diablo III launch hasn't gone as cleanly as Blizzard would have hoped. Users are complaining that they're trying to get into their new game, the long-awaited new entry in a series they've long loved, and are being met with error codes. The most common code isn't exactly game threatening – code 37 just means that the servers are full – but there are a few people suffering from a bit worse.
Gamers in Europe, for instance, are finding themselves disconnected and locked out of Battle.net thanks to error 3006. People are saying it happens when you trade with your Templar, meaning that for some it'll be easier to wait a few days before playing, to avoid any unnecessary aggro.
Thankfully, the key to the successful navigation of problems like this is communication and Blizzard are being fairly open about the issues, sharing information via Twitter and via the official forums.