I was tinkering around with the dock preferences, and found that it's possible to put non-application icons on the application side of the dock (the left side of the dividing line if the dock is at the bottom of the screen). I assume this would work equally well for putting application icons on the window/file side of the dock, but I haven't tried it.
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.]
Mac OS X Hints
http://hints.macworld.com/article.php?story=20021222140620259