Note: With dropbox, you're not really sharing a directory on your computer with the world. It syncs up the dropbox directory on your computer to the dropbox servers, which then share with the world.
What I usually do is throw what I need into the directory, let dropbox sync up, grab the public links (right click on the file), then shut down dropbox. The files will be available all the time as long as you allowed enough time for the files to upload to dropbox.