(the descriptions of various countries is based on their government system in early 2002; some of these have definitely changed since then)

Descriptions of governments can be based on:

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

 

Capitalism

(Russia)

Socialism

(Norway)

Communism

(Cuba)
In a capitalist or free-market economy, people  own their own businesses and property and must buy services for private use, such as healthcare.  Socialist governments own many of the larger industries and provide education, health and welfare services while allowing citizens some economic choices In a communist country, the government owns all businesses and farms and provides its people's healthcare, education and welfare. 

Politics - how is the government run?

 

Dictatorship

(Iraq)

Totalitarian

(China)

Theocracy

(Iran)

Monarchy

(Jordan)

Parliamentary

(Israel)

Republic

(USA)

Anarchy

(Afghanistan?)
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. Rule by a single political party. 
People are forced to do what the government tells them and may also be prevented from leaving the country. 
A form of government where the rulers claim to be ruling on behalf of a set of religious ideas, or as direct agents of a deity. A monarchy has a king or queen, who sometimes has absolute power. Power is passed along through the family 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 A republic is led by representatives of the voters. Each is individually chosen for a set period of time. 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. 

Authority - who picks the government?

 

Revolutionary

(USA, France, USSR etc)

Totalitarian

(North Korea)

Oligarchy/Plutocracy

(Pakistan)

Democracy

(India)
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 type of government (unless there is another coup or uprising). Rule by a single political party. 
Votes for alternative candidates and parties are simply not allowed. Citizens are allowed and 'encouraged' to vote, but only for the government's chosen candidates.
A form of government which consists of rule by an elite group who rule in their own interests, especially the accumulation of wealth and privilege. Only certain members of society have a valid voice in the government. This can reflect (but is not limited to) economic interests, a particular religious tradition (theocracy), or familial rule (monarchy). 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. 

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).

Much of the information on this page came from the following sources:
CBBC - Types of Government
Types of Government
How Canadians Govern Themselves
Political Systems Explained
Best Government?