IMHO, the crash on its own would have caused a recession or a mini-depression. It took bad government policy (Smoot-Hawley, etc.) to turn it into the Great Depression. In fact, anticipation of Smoot-Hawley might have helped cause the crash, then made the economy worse after being enacted.
Given that, the catalyst is merely the catalyst. Perhaps it takes really bad policy to drive a market to the point where it's vulnerable to a crash. But anything could tip it off: bad policy, shouting "fire," maybe even a killer-bee attack.