There are two empires I would place here: Macedonia and Egypt.
Of course, Macedonia was a blip on the Greek timescale. Its rise to power was shortlived. But it is amazing to think that in his thirty-some short years Alexander the Great expanded his small corner of Greece across the map, conquering even the mighty Persian empire. It is said that Caesar, in his forties, came across a statue of Alexander and felt immeasurably jealous that he had not accomplished the same in the same time.
Egypt has always been a favorite of mine. No other culture could entrance me so. A kingdom that went from a branching polytheistic religion to the worship of a single Sun god and then back to the old ways? Amazing. Plus, one cannot forget the great pharoahs such as Tutankhamen (who is given more attention than merited, but is still fascinating); Amenhotep IV, who introduced into the ancient world a true system of monotheism (Israel did not invent it, for it was itself polytheistic for many years before the chief god, Yaweh, overruled the others); and Ramses the Great, builder of many monuments.