You need to use this method.

You just need to use this method.  The important part is setting your referrer (Referring Page) to

This is about 21 gig in total…

Here is how you can download Revit 2013 using Firefox with Downthemall, and without having to Register or Login or use Akamai:

  1. Install Firefox and Downthemall
  2. Open Firefox, hit ‘Alt’ – Tools – Downthemall Tools – Manager
  3. Hit the Plus sign
  4. Paste the link you want from the list below into the ‘Download’ field
  5. Put in the ‘Referring page’ field
    (“Referring URL” in other download managers)
  6. Set your download location in ‘Save Files in’
  7. Hit Start!

Links to copy / paste into download manager:

Revit 2013 – combined

Revit 2013 – LT

Revit 2013 – Architecture

Revit 2013 – Structure

Revit 2013 – MEP

NOTE 1 – Autodesk has kinda given approval to using your own download manager before.

NOTE 2 – You could also use Flashget and manually set the referrer

EDIT – Other Autodesk product links (use referrer shown above)

AutoCAD 2013 – vanilla

Update: now try this method

Revit Architecture 2012

Revit Structure 2012

Revit MEP 2012

I recommended using Firefox with Downthemall to download these files. Finally, be sure to confirm the checksums / hashes before beginning the install.
EDIT:  Some people were having problems with these links.  However, this should no longer be a problem.
If you are interested in Student version links, go to this page.