There have been different types of political system over the history. Before emerging of modern nation-state, monarchy was prevalent however, after French Revolution Democratic republic become dominant from of political system in most of countries.
Firstly, Democratic governments are based on representation of the citizens through free-fair-regular election. Also, it protects fundamental right of human. In democratic political system, power of state is divided into three parts of institutions. Representative body such as assembly or parliament is in charge of legislation while, administration takes care of all governmental organization. Judiciary is independent from legislative and administrative bodies. Within Judiciary, there are multiple stages of courts and every citizen can appeal accordingly.
Secondly, Communist governments are based on command economy. This political system does not allow free-market regulate market and re-allocates resources upon political goal. The founders of Communist governments believe that class-less society can be built by commanding economy. However, this political system easily turns into Totalitarian government because there is on balance of power. Subsequently, freedom of speech and freedom of press is restricted in this system. Soviet Union under the Joseph Stalin, Cuba under the Fidel Castro, Vietnam under the Ho Chi Minh, Cambodia under the Pol Pot and North Korea under the Kim Jong Il is a good example of Communist political system.
Besides democratic and communist governments, there are other kinds of political systems such as Feudalism, Fascism and Theocracy. Feudalism is de-centralized political system during middle ages. The land is held in exchange for service and obedience is rendered in exchange for protection. Thus, society is hierarchically ordered. Most of medieval Kingdoms in Europe and Japan had Feudal system.
Fascism is totalitarian-dictatorship rule in the name of nationalism or certain political agenda. Germany, Japan and Italy during the World War II had this system.
Theocracy is system that government is ruled by religion. Thus, the religious leader or religious institution has more power and authority than government. Under this political system, religion is the most important criteria to make all decisions in a society. Generally speaking, Iran is belonged to Theocracy.