Is there some application to download files from popular file hosting websites?
Firefox has an add-on for that purpose, called Skipscreen.
Description from AMO:
Skips unnecessary pages on sites like Rapidshare, Megaupload, zShare, Mediafire, and more. Try it out, or watch a demo at http://www.skipscreen.com
Why click through ad-laden pages and wait for countdowns when your computer can do it for you
Plowshare
My favorite is plowshare -- see here for installation instructions.
It's a command-line tool, very fast and efficient (as opposed to JDownloader, which was always extremely slow for me, probably because it uses the Java VM).
Example
plowdown http://www.mediafire.com/?9i282l2o6f27enw
Starting download (mediafire): http://www.mediafire.com/?9i48232o6f27enw
Leave this field blank and hit enter to get another captcha image
Enter captcha response (drop punctuation marks, case insensitive): example captcha
File URL: http://199.91.153.74/mg1jopw993tg/9i48232o6f27enw/Example.pdf
Filename: Example.pdf
% Total % Received % Xferd Average Speed Time Time Time Current
Dload Upload Total Spent Left Speed
100 180M 100 180M 0 0 125k 0 0:24:35 0:6:35 --:--:-- 458k
Example.pdf
Note: captchas appear in a separeted window on the desktop using Image Magick.
Features
plowshare supports many different websites through plugins.
A small footprint (few shell scripts). No JAVA. Run fast on embedded devices!
Few dependencies and portable. bash and curl are enough for most hosters.
Modules (site plugins) are simple to write using plowshare API.
Support for automatic online captcha solver services.
Source: https://github.com/mcrapet/plowshare/
JDonwloader does exactly that - with some capthca skipping (that doesnt work on all sites)