Politics
How is the government run?

MONARCHY: A monarchy has a king or queen, who sometimes has absolute power. Power is passed along through the family.

PARLIMENTARY: A parliamentary system is led by representatives of the people. Each is chosen as a member of a political party and remains in power as long as his/her party does.

DICTATORSHIP: Rule by a single leader who has not been elected and may use force to keep control. In a military dictatorship, the army is in control. Usually, there is little or no attention to public opinion or individual rights.

REPUBLIC: A republic is led by representatives of the voters. Each is individually chosen for a set period of time.

ANARCHY: Anarchy is a situation where there is no government. This can happen after a civil war in a country, when a government has been destroyed and rival groups are fighting to take its place. 

FEDERAL REPUBLIC: A federal republic is a federation of states with a republican form of government. A federation is composed of a number of self-governing states united by a federal government.

CONSTITUTION: A constitution refers specifically to a national constitution, which defines the fundamental political principles and establishes the power and duties of each government. Most national constitutions also guarantee certain rights to the people.

Economy
What provides the goods and services that are bought, sold, and used?

COMMUNISM: In a communist country, the government owns all businesses and farms and provides its people's healthcare, education and welfare. 

SOCIALISM: Socialist governments own many of the larger industries and provide education, health and welfare services while allowing citizens some economic choices.

CAPITALISM: In a capitalist or free-market economy, people own their own businesses and property and must buy services for private use, such as healthcare.

Authority
Who picks the government?

DEMOCRACY: In a democracy, the government is elected by the people. Everyone who is eligible to vote - which is a majority of the population - has a chance to have their say over who runs the country. 

REVOLUIONARY: The existing structure is overthrown by a completely new group. The new group can be very small - such as the military - or very large - as in a popular revolution. After a period of time, this 'becomes' one of the other types of government (unless there is another coup or uprising).

COMMONWEALTH: a commonwealth is an organized territory that has established with the Federal Government a more highly developed relationship, usually embodied in a written mutual agreement.

REMEMBER: nearly every country in the world is ruled by a system that combines 2 or more of these (for example, the USA is not a true capitalist society, since the government actually provides some services for its citizens). Additionally, one person's opinion of the type of government may differ from another's (many argue that the USA is actually a plutocracy rather than a democracy).