According to various players on the battle.net forums, Diablo III has had it's first major bug discovered...and it's pretty bad.
Apparently, the bug will boot players from the game and refuse them reentry under any character until Blizzard fixes it for you.
The bug, which leads to an 'Error 3006' message, can be caused by trading your currently equipped shield with the Templar NPC and was, apparently, one of the bugs reported during beta testing...that was just not fixed I suppose. That's the price you pay for being the first to play the game though. I'm sure it'll all be fixed in no time.
More info on the bug can be found over at the battle.net forums.