API page: http://api.drupal.org/api/drupal/modules%21system%21system.api.php/funct...
Enter a descriptive title (above) relating to function hook_menu_alter, then describe the problem you have found:
Sorry, I submitted a comment on the documentation before seeing that it's best to file an issue instead. Fee free to delete that comment.
However, I think this menu item only shows for anonymous users, users for whom user->id == 0 I believe that the 'user login' and the 'request new password' pages ( and menu items) are hidden by default for authenticated users, so this may not be a very good example.