The dynasty of Akkad was regarded in such later tests as the Sumerian King List as a family of city-rulers who held kingship over Sumer and Akkad in the same way as many other dynasties that came earlier. The nature of its rule was very different from what preceded it, however, and temporarily it ended the system of city-states that had characterized Babylonia until then. The processes of political centralization in Babylonia and the spread of Babylonian influences throughout the Near East evident in the Early Dynastic period attained an unprecedented climax. Moreover, never before had Babylonian armies systematically campaigned that far, and had the political dominance of one city been so great. Mieroop, p 64
Ruler
Time
Description
Sargon
BCE - BCE
Sargon was a commoner who rose to prominence in the city of Kish. He likely usurped power, taking the throne title the king is legitimate. Sargon later moved the center of his rule to Akkad but his two successors still kept the title King of Kish. The city Akkad remains unfound, but it was almost certainly in the north of Babylonia (perhaps beneath modern بغداد Baghdad) -- an ideal location from which to rule Babylonia and control the the Near East, though further north than conventional Sumerian city-states. He was the first to implement the use of Akkadian and not Sumerian as the administrative language of the empire.
Rimush
BCE - BCE
Manishtushu
BCE - BCE
Naram-Sin
BCE - BCE
Naram-Sin denoted himself as not a liaison to or close to the gods, but as an actual god himself, which was a breakthrough event. He is also famous for the Stele of Naram-Sin and perhaps as the subject of the Bronze Head of Sargon / Naram-Sin.