One of the greatest historical rivalries to have ever occurred was between the Sassanid and the Byzantine Empires in between 3rd and 7th centuries. These two gigantic empires fought one another in many bloody wars. However, they also did not manage to defeat the other one totally and had to learn to coexist with one another.
The Sassanids are particularly very interesting in this regard in that they were the continuation of ancient Iranian empires that had dominated the Persian plateau for centuries. Starting with the Achaemenid dynasty, Iranian culture had been a thorn in the side of the Romans.
This video by the EmperorTigerStar goes over the many wars that the who fought in the years before the Muslim conquests.
Byzantine-Empire.com 