Fixing instance server errors
You may have seen this same error what9000 is getting every time he tries to enter an instance: he gets bounced out of the portal and "Additional Instances Can't be Launched" pops up on the screen. Just in case you've never quite heard exactly how the game works, the World of Warcraft is actually a series of servers, and as you travel across it, you contact more than one system of computers. Your realm is one group of servers, but within that group, there are many different computers sending information to and from yours -- when you're in Azeroth, you're talking to one server, when you go out to Outland, you visit another, and in Northrend you're on yet another. And there are even servers that track non-location information: how much money you have, what you're wearing, and so on.
Likewise, instances have their own system of servers, which is why you can sometimes be in an instance when the world server "outside" will go down, and if you leave that instance you'll get disconnected. And Instance servers can be overloaded as well. This error message is likely a way for Blizzard to keep from crashing the instance servers -- if too many instances of a dungeon have already been created, new players trying to get in are not allowed.
However, as a few people say in the comments of what9000's post, there are some client-side fixes as well. Sometimes, the Instance server will lock you out just for a single instance's creation, so resetting the instance on your side (by leaving a group and rejoining) will sometimes clear things up and let you in. It's not impossible that Blizzard's servers are overloaded (we should see a nice bump of new players this weekend, after the holiday), but if you're seeing this message constantly, even during slower times, something is likely wrong.
