To do this, navigate to ~/Library/Preferences and open com.apple.dock.plist, either in a text editor (if you know XML) or the Property List Editor (which I believe requires the developer tools be installed).
You will see a key under the root called "persistent-apps" and one called "persistent-others". "persistent-apps" contains all the application icons (on the left side of the dock divider) and "persistent-others" contains all the, well, others. Popping open one of the children of either of these will show you all of its information, including its name. This will let you find the item you want to move. To move it, just copy all of the information from "persistent-others" to a new child of "persistent-apps", being sure to give it a new number so you don't overwrite any existing application launchers. Save the file and log out and back in (or just kill the dock process).
I used this to put my dock menu of applications on the left, next to the Finder icon. (Unfortunately, you don't seem to be able to move the Finder or Trash icons via this tip... I'd love to have been able to put my menu on the far left of the dock.)
[Editor's note: I have not tested this hint. We had an earlier hint on this subject that pointed to a discussion thread on the MacNN forums which is now broken, so I'm publishing this one as a replacement.]

