Help! My patch isn't downloading? It's stuck at 68%/73%/xx%!
It probably is downloading -- be patient and let it run. Blizzard uses a Bittorrent-based system to distribute the game's patches through the official client, and those systems depend not just on Blizzard and their ability to distribute the patch, but also how much of the patch all of your peers have. If everyone around you has xx%, that's all you'll get for now. But an hour from now, someone will have spread the full patch around, and then you'll pick it up no problem. Patience is a virtue, and until the realms come back up, you can't play anyway.
Also, the patcher will stop showing progress around 70% or so -- at that point it'll start installing the patch, and you'll need to click another button to see installation progress. But if you just let it run, it'll update.
What does "The tracker is not responding" mean?
Another Bittorrent issue that should resolve itself after a little while. The patch will need some time to disseminate, and if you get a message like this, it just means your client hasn't found all of the connections that it can. It will.
I get a weird "Unable to Validate Game Version" message when I log in. Is my client broken?
No. Blizzard's servers aren't all upgraded yet (hence the reason we can't play). When they are all upgraded, your client's version will match the server's, and everything will be hunky dory.
I downloaded the patch fine, but I get a message saying "The file WoW.exe could not be found." What's up with that?
This could be a more serious problem (you may need to run the Blizzard repair utility, or even reinstall the game), but you won't know for sure until the realms are back up and running. Wait until Blizzard has gotten the servers back up and running, and then try to run the client/install the patch again. If you still have issues, then it's time to run the repair utility (which should be in your game's folder), and see if there are other issues happening -- could be anything from a bad hard drive sector to a corrupted client.
Note: Don't bother running the repair utility until the servers have come back up -- the repair utility likely won't recognize your client right now, either. See the next answer.
I have some other issue, but Blizzard still hasn't gotten the servers back up! Should I be worried?
No. We've almost never seen Blizzard have problems with the patch updater and the release to the live servers. 99% of the problems we're seeing right now will be fixed on their own when the servers return with their updated software, so your best bet right now is to be patient, let the patch make its way out to everyone's client, and let Blizzard do their thing with maintenance. If the servers go back up and you still can't connect or download the patch, then it'll be time to head over to their Technical Support page and start figuring out what might be wrong.