The classic study of the depression by Milton Friedman and Anna Schwartz, decades later, made a convincing case that it was caused by the US central bank pumping too little money into the economy, not too much.
Some historians (including Milton Friedman and Anna Schwartz) blame the market crash of 2nd half 1937 (U.S. stock prices fell by 40%) and the Roosevelt recession on the Federal Reserve signaling from late 1936 that abnormal monetary ease would end (raising reserve requirements).
But if Milton Friedman and Anna Schwartz were right in their insistence that it was actually the Federal Reserve that caused the Great Depression (which is something that Ben Bernanke himself has insisted that the Fed will not repeat) then one way of interpreting what has happened is that the European Central Bank has just set us all up for another Depression.