Why do governments exist?

Okay so why do governments exist? The cynic in me says to enrich the elected officials involved in the business of government but that would be too negative...

In medieval times the role of government was to protect and enrich the king.

More recently, according to the US Constitution the role of Government is to protect the 'natural rights of people'. Just what are the natural rights of people? That appears to be greatly debated between liberals and philosophers through the ages (a topic for later inquiry).

I like a more practical definition based on the fact that government is 'for the people, of the people and by the people'. I think governments should exist to represent and support the people in their pursuit of ever increasing national prosperity.

By national prosperity I don't just mean wealth. My broader definition of national prosperity is:

The degree of peace, happiness, security, health, education, community, wealth, environment, individual freedoms and economic opportunity available to a nation's citizens.

Now I'm not advocating that government be solely responsible for providing and increasing national prosperity (this would likely fail, just ask Soviet citizens how the 1980's went). Rather government's should pursue, facilitate and protect the pursuit of higher national prosperity by the nations citizens.

So in defending the nation against invasion, the government has a role; in ensuring the corner store has milk at 6am, not so. And in between is well, in between depending on your political view of the world...