I should have studied History instead of mechanical engineering
This intrigues me now. Especially after the likes of Blue Mythril's reply!
With loose definitions of 'great' and 'power', size and strength and span of time, the Romans must win hands-down. The fewest number of individuals 'controlling' the greatest number of others.
As to cultural influence, religious influence, scientific advancement, border influence, single personal emperor and so on, each has a different answer.
Eight thousand years of China (imagine what that means)... Christianity brought down the Egyptians... Persians influenced all surrounding nations and empires for a great length of time. Without them, I doubt if anyone else would have had the 'drive' to advance civilization, or organization, or knowledge... All of these things give us the story of human civilization. Somethings are re-invented, some things deserve credit to one peoples or a single great mind...
The greatest empire of all is the human brain. Nothing this Earth can offer will defeat its cunning. At least not for a very long time to come.
And my picture of the future? The geatest empire of all will have to be man as an agreeable single unit. The Earth is too small to hold so many people who fight each other. Diversity, sure. Freedom, sure. But there is no freedom without Law. And with upcoming technology, smaller more devastating bombs, and short vision, Rome will be our only testament of a 'great' empire. For we may have destroyed ourselves all too soon...
Apologies for the lecture, folks. But if we appreciate the past and wonder at Empires of old, imagine how someone might ask the same question 2000 years from now......