Windows only: If you use Dropbox to share files with your friends, free app DropPub makes it even easier by adding an item to the context menu, from which you can make any file public and add its link to your clipboard.
To set up DropPub, just download the zip file and extract it anywhere on your system (its location will be permanent, so I put it in Program Files). Then, create a shortcut of DropPub.exe and name it something like "Dropbox Public Folder". Then, move that shortcut to your %APPDATA%/Microsoft/Windows/SendTo folder.
Now, when you right-click on a file anywhere in Windows Explorer, you can go to Send To > Dropbox Public Folder and it will copy the file to your Public folder. It will also copy its public link to your clipboard, so you can immediately add it to an IM, email, or wherever else you want to send it.
The first time you invoke DropPub, you'll need to enter your Dropbox public ID (the number that comes after /u/ in a file's public URL) and the location of your Public folder on your computer. After entering that information once, you won't have to do it again. Check out the video for setup instructions and to see it in action.
Update: The developer of DropPub has updated it to fix a bug with spaces in a filename and to make the install process a bit easier. Hit the link to download the updated version.
DropPub [Autohotkey tools by fwinkelbauer]