The Great Depression was the result of a misguided government policy of the Hoover administration: after the economy went into a recession triggered by the stock market crash in 1929, taxes were increased to 50% with the goal to reduce the budget deficit, and even worse, the money supply was allowed to decline by 31% between 1929 and 1933, nothing was done to stop the panic and loss of confidence caused by bank failures, and protectionist measures were introduced to protect the domestic economy (Hawley-Smoot Tariff Act). These policies transformed the recession into the Great Depression.
Today's government policy is designed to ease the effects of the recession by restoring consumer and business confidence, implementing expansive fiscal policies, increasing the money supply, and fixing the financial system as a matter of priority, even if it means a higher budget deficit and government debt, and a higher risk of inflation in the future.
It seems that these policies may begin to work. In fact, there are indicators which predict that the US economy may be closer to a recovery. Although there is still a considerable downside risk that the economy may get worse before getting better again, it is highly unlikely that the economy will go into a depression like the one in the 1930s.