Our sister site Big Download has mirrored the files necessary to update your game client to patch 3.1. Only the PC version is up at this time, however they're working on getting the Mac version.
Many users are reporting inability to finish the download via the Blizzard downloader or are generally having problems get their own copy of the patch.
All you need to do is go and download this file, install, and you'll be set to enjoy all the patch 3.1 goodness.
Update: You can now download the Mac patch files as well. Enjoy!
Update: You can now download all the international patch files.
Comments have been disabled for this post.