Not only can you change your desktop folder, you can change the location of any other folder Ubuntu creates for you in your home folder, like Documents or Music – and this works in any Linux distribution using the Gnome desktop manager.

In this example, we’re going to change desktop to show our Dropbox folder. Open your home folder in a File Browser by clicking on Places > Home Folder.

In the Home Folder, open the .config folder. By default, .config is hidden, so you may have to show hidden folders (temporarily) by clicking on View > Show Hidden Files.

Then open the .config folder by double-clicking on it.

Now open the user-dirs.dirs file…

If double-clicking on it does not open it in a text editor, right-click on it and choose Open with Other Application… and find a text editor like Gedit.
Change the entry associated with XDG_DESKTOP_DIR to the folder you want to be shown as your desktop. In our case, this is $HOME/Dropbox.
Note: The “~” shortcut for the home directory won’t work in this file (use $HOME for that), but an absolute path (i.e. a path starting with “/”) will work.

Feel free to change the locations of the other folders as well.
Save and close user-dirs.dirs. At this point you can either log off and then log back on to get your desktop back, or open a terminal window Applications > Accessories > Terminal and enter:

killall nautilus

Nautilus (the file manager in Gnome) will restart itself and display your newly chosen folder as the desktop!