In chronological order
1) Ancient/Greece - ancient Greece that is, conquered "the known world", resulting in the Hellenic Age, and made huge advances in philosophy, etc... who passed the torch to...
2) Classical/Rome - Pax Romana, who passed the torch to... after a LONG delay...
3) Medieval/France - Lingua Franca became the most important language in the world for a reason...
4) Industrial/England - the sun never set on the English Empire in it's heyday, including setting the stage for...
5) Modern/America - the leader of the FREE world, countless innovations/inventions, the American dream, and English being the lingua franca
Of those, France is my most likely to be replaced...
6) Future/???
If I were to replace one, it would be France, with either Arabs or Byzantines, these two forces were making advances while W. Europe was having a rather rough time with things.
I accept that my list is completely eurocentric, but let's be honest, the civilizations with the biggest impact on history generally are...
I didn't pick China because outside of their area, they haven't really been a big deal... China has always been inward looking.
Egypt should definitely not be on the list, WAY overrated... their culture was never really adopted anywhere for a reason. No real influence. They left some startling monuments, and some pretty stuff... but...