The gdmlogin program has a menu on the far-right of the menubar with
entries like shutdown and reboot (I think the menu is called "system").

It would be useful if I could add my own entries to this menu to execute an
arbitrary command.  For instance, I run gdm on a remote X session, and I
want a menu option to shutdown the local machine.  If I could add an entry
to the menu to rsh the local machine and issue shutdown, it would give the
impression that this was a system command (where the shutdown option is
usually expected to appear), rather than having to do this as an Xsession
or create a user that executes a script on login.

It could also be useful for simple things like pinging a remote host to see
if it's alive or running a clock program.