Blizzard is well aware of the realm issues that are plaguing the game tonight, October 21st. They have said in the opening in-game announcement that they're working on it, and now have posted as much on the forums. They will also be restarting all realms shortly.
For those of you not experiencing the issue, just about every time you try to enter an instance you receive a "transfer aborted" message or some other such error. This is causing quite a bit of havoc on guild as they try to push hard during the last few weeks of Burning Crusade raiding.
We'll update this post throughout the evening when Blizzard releases any more statements.