With all the media attention given to the 2013 US Federal Government shutdown, one might be inclined to think this was a rare occurrence.
The truth of the matter is that the US government has shut down 18 times since 1976. The source of a government shutdown is related to the particular way government funding is enacted. Government funding is the responsibility of the Congress according to the "separation of powers" concept in the US constitution. Each year congress needs to pass the "appropriations bills" which apportion budget to government departments for them to operate.
Any disagreement between the congress members, or between congress and the president, that cannot be resolved can lead to these bills not being signed. When the bills are delayed beyond the point where the existing bill expires, funding for government stops and departments are required to shut down.
Generally these shutdowns have been of low impact and often fell over a weekend while the congress members negotiated a compromise.
However, the most significant shutdown was the 21 day shutdown in December 1995 when congress and President Carter fought over the budget deficit. The second longest shutdown was the 16 day closure in 2013 which centered around the new "Obamacare" health system.
Both these shutdowns affected around 800,000 government employees.