Did Roman's used to have kings or emperors?

They had both. At the beginning of the city they were ruled by kings , they overthrew the kings and formed the republic which in turn was replaced by the emperors.

To add more information here as a minor edit, for almost 500 years before the principate of the first emperor, Augustus Caesar, the republic mentioned above was the government of ancient Rome. In speaking about such a long period of time, the Roman Republic altered itself to meet the demands of the times. The republic was basically a system where the balance of governing powers was shared by a Senate, a popular Assembly, and elected Consuls to execute policies and recommend new ones. For most of the time under the republic, wealthy senators held sway over public policies. The time of the republic was a complex system and ever changing. Under the laws of the republic, at times of critical problems for Rome, a person could be named "dictator" under the belief that one man rule was at times the fastest and best way to protect the republic. No time could be spared by having issues of major importance be a debate . This office of dictator was one of brevity so one man could not dominate the government for too long a time. Just prior to the beginnings of the "emperor" period, other government constructions were made such as the two Triumvirates where three highly respected leaders shared in the rule of Rome.