This thread on ETS has been fantastic for keeping people abreast of support information, and I'll summarize the main points here:
You can download all 36 tracks from Amazon.com for $5 if you're in the USA, and here is the accompanying PDF. You can get the other bonus digital stuff via the torrent above. The Amazon download is a lower bitrate, and the MP3s don't have the individual artwork.
If you want a quick fix, download the first 9 tracks & digital extras via The official NIN Pirate Bay account.
If you've used up your three downloads, contact email@example.com, although you'll likely get this response:
Due to overwhelming response, you probably have experienced technical difficulties purchasing or downloading your copy of Ghosts I-IV. We are currently working diligently to address these issues, and will do everything in our power in ensure that your download will be successfully completed.
If you have hit your download limit, we will be resetting the download attempts as we resolve the technical issues within the next 24 hours.
We do apologize, and thank you for your interest and response to our offerings to the fans of nine inch nails.
If you were having troubles, but they have been resolved, please click the link in your support email and close your ticket. This will allow the support team to skip over your request and get to someone who still hasn't been able to download faster.
If you ordered via www.ainr.com and have not received your download link, don't fret, no one else has:
[You'll] get [your] download - it's supposed to be immediate, for one reason or another it's going to be a little while before downloads are sent out for those orders.
For more information, visit the Ghosts I-IV forum on EchoingTheSound.org.