SUDO (superuser do) should do the trick, if you're not using any mainstream Desktop manager like KDE or Gnome (which would have the option in its 'start-like' menu). Just configure sudo to let some users/a user group to execute a command or series of commands. Then the box will ask his/hers password, not root's. Or no password at all.
Some more reading on SUDO (the linked archive page has many links to various pages about SUDO or SUDO configuration) [NetBSD Archives (a Linux question)]