Well, okay, so I don't know that the title of this post is strictly true: you may be able to run the Adobe Updater even if you're not logged into Windows as a user with administrative rights--but I don't know how you launch Adobe Updater other than from the Help menu of an Adobe product and the point I'm really making in this post is that if you aren't logged into Windows with administrative rights, you either won't have the menu option "Check for Updates" (this was the behavior I observed in Adobe Acrobat and Adobe Reader) or the menu option "Adobe [Product Name] Updates" will be "grayed out" and unavailable to be selected (this was the behavior I observed in Adobe ColdFusion Builder).
So the point is this: make sure you're logged into Windows with administrative rights if you want to update your Adobe products! If you find this same behavior on another operating system, please post a comment to let me know.
I'm posting this because when I searched to figure out what the problem was, I couldn't find anything; fortunately, it dawned on me what the issue was. But some keywords for search engine indexing are in order here: Adobe Check for Updates menu item not shown, Adobe Check for Updates menu item not available, Adobe Check for Updates menu item not there, Adobe Check for Updates menu item missing, cannot run Adobe Updater.