This Economist piece pins down the distinction between recessions (2 consecutive quarters of negative growth) and depressions (declines of GPD which either exceeded 10% in a year or which persist for more than 3 years) and analyses when and where they each occur. Depressions were more common in the past because bank failures were more often permitted and because the share of government in the economy was smaller. These days depressions are much more common in emerging economies - Russia had a dozy 1989-1998 when GDP fell 45%. ASEAN countries experienced depressions following the 1997 Asian crisis.
It remains an open question whether the US will experience a depression now. Most economists say not (fiscal actions and support of financial institutions the reason) but in the current disturbed environment these forecasts have limited (I would say close to zero) value. Model-based forecasts are only valid in the range of experience the models are based on and the current situation is something distant from recent experience. What is true is that the US economy declined 6% on an annualised basis in the December quarter.
The price paid at Intrade for a US depression outcome implies a depression probability of about 30% compared to a probability of 10% in November 2008. See: