I am interested in reading about the worst economic crisis of all times. By that I mean the largest reduction in GDP over a period of at least a year. The economic crisis should not have been caused by war nor natural catastrophe, but events that could arise arise in a stable society today, like a financial crisis, economic mismanagement or similar.
The Economist illustrated the History of World GDP by way of the intriguing graphic below.
The mismanagement of the Chinese Qing empire between the years of 1820 and 1913 is plain to see. Similarly, assuming that colonialism satisfies the OP's criteria, the difference in percentage GDP of (British) India between 1700 and 1940 is simply astounding.
Up front, imho GDP and "like a year" is not really suited for objective comparing of historic economic crises, which run on time scales of at least several years or a decade, smaller time scales are better called economic fluctuations. Comparing economic crises in different historical epochs, national and world-wide ones, by proportional (%) GDP reduction might turn out a bit tricky, due to incomplete data and different assessment basis.
But anyway, regarding economical, poltical mismanagment or faulty construction of economic system by pure better-known numbers, the biggest economic crisis was the Great Depression
Austrian economist Kurt Richebacher states in a economic analysis of the Great Depression (the whole article is worth reading):
"Smaller/national" examples in 20th century would be:
For crises before 20th century a look on these examples might be interesting:
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The Great Depression of 1929-1933 showed a fall in real GDP in the United States of 38.1% according to this source. This was probably the greatest fall in real GDP in the independent history of the US, although the Panics of 1796 and 1819 could have been larger.
Beyond the US, Britain's biggest recession was the 25% fall following the end of the First World War, which exceeded the 5.8% fall experienced there in the Great Depression.
Some areas of the former Soviet Union experienced a 45% fall in GDP after the transition from planned and globally integrated economies to isolated and market oriented economies.
Going further back, the Great Depression of the 14th century in Europe led to a fall of up to 40% in some countries.
I would say that the worst economic crisis was the Great Depression of the 1930s because it was global. Individual countries had worse experiences, but these were individual experiences, not worldwide.
Other answers discuss the economic specifics in greater detail but here were some of the political results: 1) The rise of Adolf Hitler in Germany. 2) The concurrent "hobbling" of European economies that prevented them from rearming to resist Hitler (Germany followed a "Keynesian" policy whereby re-arming actually "pump-primed" its economy but few people understood that at the time) 3) Other "have not" nations like Italy and Japan "ganged up" with Hitler's Germany against the rest of the world (these were actually rich nations that were "have not" only in comparison to the United States or Great Britain).
The reason I say that the 1930s economic crisis was the worst of all time was because it led to World War II. It actually arose out of the seemingly "stable" environment of the 1920s. There is at least one economic writer who believes that we've seen the modern 1920s, and are headed for the modern 1930s. http://www.financialsensearchive.com/editorials/au/2006/0509.html
One of the hardest was possibly the crisis in Russia due to introduction of Capitalism, the breakup of the USSR in 1991 and pro-American policy of the Yeltsin's government.
This is the drop of GDP per captia:
This is graphic depicting the drop in industrial output in Russian Federation (blue) and Moscow (red), in per cents to the level of 1991:
This graphic shows index of machinery production of Russia, in percents to the level of 1991:
This graphic shows the GDP per captia of Russia (blue) and the constituents of the USSR (red) in 1950-2010 conpared to that of the USA in the same year (in purshasing parity prices).