According to author and historian Tom Woods, the answer is yes.

Free market defenders will often make the claim that had the government not attempted to stem the current recession, we could likely look forward to a downturn of a couple years.  However, evidence of this never accompanies.

In the speech below, Tom Woods does provide such an example.  According to Wikipedia on April 12, 2009:

http://en.wikipedia.org/wiki/1921_recession

The recession of 1921-1923 proved to be the sharpest economic downturn since the emergence of the business cycle in the early 19th century, but it also was one of the shortest reversals. The government intervened minimally, wage rates were permitted to fall, and government expenditures and taxes were reduced. The recession was over in one year.

Does anyone have examples of prolonged depressions that occurred without a government stimulus or banking system shenanigans?