Monarchy
A monarchy is defined as a system of rule by a monarch. A monarch is generally a king or a queen who has power over the state and its subjects. It is passed down hereditarily.
Oligarchy
This is rule by an elite few. It can include royal families, nobility, aristocrats, and corporations. Oligarchies can be an aristocracy. Aristocracies are usually royal families, nobility who owned land, and certain classes that hold power (political or religious). Oligarchies can also be a plutocracy, or rule by the wealthy few. Royal families are plutocrats, as are wealthy representatives in democratic nations.
Democracy
This is rule by the people. Examples are democratic constitutional republics, like the United States, and capitalist social democracies, like the Scandinavian countries of Denmark, Sweden, and Norway.
Dictatorship
This is the rule of one person in a position that grants them absolute power. The current reign of Bashar al-Assad in Syria is an example of a dictatorship.
Totalitarianism
This is the total control of society by the state, eliminating any democratic aspect. The fascist governments of Germany, Italy, and Spain during World War II are examples of totalitarian governments.