This originally appeared on the Annexe.
UPDATE 2018: Can’t do this anymore! I guess it was too simple to use.
From the text file
How to use the Public folder.txt in the Dropbox public folder:
The Public folder lets you easily share single files in your Dropbox. Any file you put in this folder gets its own Internet link that you can share with others – even non-Dropbox users!
Step 1: Drop a file into the Public folder.
Step 2: Right-click this file, then choose Dropbox > Copy Public Link. This copies an Internet link to your file that you can paste anywhere: emails, instant messages, blogs, etc.
That’s it! To share your file, just send the link to a friend.
Happy Dropboxing! - The Dropbox Team
P.S. You can only link to actual files within your Public folder, not to folders. For help with sharing files visit http://www.dropbox.com/help/16