If you are one of the millions (?) of poor souls (Diablo III players) wondering "why can't I log on to my local Battle.net server?" or "what the f**k is an 'error 37' or 'error 3003'?" then you need only look to Battle.net's various pages designed to keep you from losing your mind. First there's the server status page which tells you if the server in your region is up, down, or downright lost in the ether. This will at least keep you from wasting your precious time attempting to log in when it's not possible.
Then there's a rundown of common issues that players are facing in this handy dandy list. Finally if you want to know what all these crazy error codes are, then you can look through this list on Battle.net. Knowledge is power, as they say.
While we feel bad for the trouble that Blizzard and Diablo III players are having today, all this login trouble on launch day can be attributed to the questionable decision of using an always connected to Battle.net scheme that the company decided to go with. I'm sure over time this may not be a problem but when you have so many people trying to play the game at once it's easy to see why bad things happen to good people.