Black Tuesday was the result of a confidence in the market that was suddenly shattered. When the confidence disappeared, banks became unwilling to hand out loans and the economy stagnated. But that only happened because there was nothing to indicate that the market could be headed for a downturn. At the time, the only metric economists used to evaluate the health of the market was the Dow Jones Index. Economist Irving Fisher somehow had the guts to say "stock prices have reached what looks like a permanently high plateau" shortly before Black Tuesday.
When that confidence was suddenly shattered, the market almost completely collapsed. The signs were there - the 1% owned more wealth that it ever had before and bubbles were formed - but at that point the economic system hadn't developed enough litmus tests to monitor the health of the Stock Market and the American economy.
That probably won't happen again. These days, we have a whole industry based on measuring the relative strength of the financial system instead of just looking at the mean value of 30 stocks. Confidence in the system is essential for a healthy economy. The Great Depression, much like the Titanic, led to the adoption of safety measures across the board that protect investors and the companies they invest in. Companies like FINRA prosecute investors and companies that aren't playing by standards that were set in response to the great depression. The SEC both dominates college football and operates as a public defender of the integrity of the market. Because of the battle in the courts between the SEC and private corporate lawyers, generally the bankers who play by the rules intelligently prosper and those that don't fail.
So yes, there will be recessions. Bubbles will pop and people will default on their loans and the market will crash. But because of the rules set in place after the Great Depression, it is unlikely that this country will see a catastrophe on the same scale again.