Archiving papers, simulation and experimental data, etc?
I have a similar approach with folders, with two additions:

Everything goes into a revision control system.  In my case, I've got some things in Subversion repositories, and others in Mecurial repositories (I've also dabbled with Git, but haven't made the final transition).  The benefits of revision control are that you can always go back to a previous version, you won't have old versions littering your folders, and sharing with collaborators is relatively easy.  This should take care of your duplicated-file problem.

I also use Dropbox extensively, in order to have my files available on any computer at any time.  Dropbox provides a modicum of version control (30 days worth), but it should not replace a proper revision control system.  It does provide a cloud-based backup of your work.
Finally, regardless of how you're keeping your work arranged, make sure you keep an off-site backup (e.g., via Dropbox or personally-controlled media).