Object Doct or Object Dock Plus?  If plus Zoomer or Tabbed Dock? 

Sounds like the Zoomer Dock.  When this happens do you open up the dock configuration and see what the position option is set at?  It may be that all you need to do is just reset the position setting and not close out and restart the dock.

Just plain Object Dock (not plus).  If I go to the settings (when it has shifted to the right), it is properly set to "center" - I tried changing it to right or left and back to center again, but it remains stuck on the right no matter what I do to the setting.

(The primary game I play where this happens is Warcraft 3 - I can play it in widescreen resolution, but everything gets stretched.  I have no problems playing it in a 4:3 res other than this OD issue...)