Sumeria, in Mesopotamia, is generally regarded the worlds oldest civilization. It was separate city states though so it was not considered one unified civilization like Egypt after Menes unified it. Egypt is usually considered the second civilization after the Mesopotamian Sumerian cities. I think the Elamites and the Nubians then come after that in that region, though the Harrappan civilization in India is probably almost as old as Egypt.
“With Heaven's aid I have conquered for you a huge empire. But my life was too short to achieve the conquest of the world. That task is left for you.” ~Chinggis Khaan
It really depends on how you define "civilization". There were neolithic cultures who built rather large cities, used lime to decorate their floors and stone houses' walls, built quite complex underground irrigation canals, yet they're not considered civilized, because they haven't invented writing yet.
And then you always have the crazy people, who discover a scratched rock in some cave in their glorious homeland and call it a clear proof that their stone age ancestors knew how to write, therefore they're the most awesomest oldest civilization on earth.