The Antikythera Machine is so remarkably cool -- it is as complex as any machine humans could create up until the 14th Century. There are tendrils that possibly connect it to Archimedes or his School.

Classical Greece was millenia ahead of the rest of the world. Pindar writes of the automata found in Rhodes:

  The animated figures stand
  Adorning every public street
  And seem to breathe in stone, or
  move their marble feet.

There was even a working steam engine in Alexandria before it was burned down: http://en.wikipedia.org/wiki/Aeolipile