Now the Greeks had a lot of different types of governments since you had many city-states in Greece and hence each of them had their own respective Ancient Greek Government. Also, the idea which people had with respect to what constituted a good government kept changing over the times.
Ancient Greek Government
According to Aristotle, the ancient Greek government was divided into four: oligarchies, monarchies, democracies and tyrannies and the current historians actually use for or less the similar divisions.
Now there was a certain pattern which the government followed according to the time it was set up. The monarchies were the ones which came up first and this was followed by the oligarchies, which was followed by the tyrannies and finally the democracies.
But then every period had a lot of city-states which had different systems and many were present which never any sort of tyrannies or democracies became.
Who ruled ancient Greece
In the Bronze Age (late) which was around 2000 and 1200 BC, the Greek states had monarchies which were ruled by kings. Greek mythology, as well as Iliad, was written by Homer, gives us a picture of kings who ruled like Agamemnon and even Theseus. Some archaeologists have also managed to dig up quite a few places. Now right after the era of the Dark Age, very few cities had ancient Greek governments with kings.
Among these Sparta was the most well-known one, which had not one, but two kings, who were brothers or even cousins. One of them would stay at home and the other would go off to war and vice versa. Now in the Archaic period, the cities were ruled by the oligarchies which refer to aristocrats or a group of rich people.
Also from the 600 to 500 BC, the cities were dominated by the tyrants. Tyrants referred to the aristocrats who managed to overpower the kings after getting a lot of support from the common people. They would look after the ancient Greek government like kings but without having any actual legal right to do so and finally in 510 BC the domestic government had come up.