I got my start playing on the Amiga version of Empire, which had a "patrol" feature, where you could set the piece to automatically move between two points with no user interaction until an enemy piece was detected.  I couldn't find anything in the current Classic Empire like that, other than "move randomly."  Is there a Patrol feature?  I loved it.

I have to second this.
Airplanes had Patrol "flight paths" (different from "Supply lines" where you could
shuffle planes to the front)
I know Destroyers and Submarines could "Patrol"; not sure I ever tried it with
other ships...

Version 2.05C 24-Oct-88 is my favourite version and it has a patrol feature: http://www.the-underdogs.info/game.php?id=368