In a word, zero.
I'm not saying there won't be a bear market, there will, but a calamitous single day crash is out of the question. Why?
*Downside trading curbs placed on the Us exchanges as happened briefly last night
*The existence of the President's Working Group on Financial Markets (AKA Plunge Protection Team or PPT) (the influence of which, is hotly debated)
*The uptick rule on short selling stock
That's off the top of my head, but there are other measures, structural, and value differences between then and now.
This doesn't mean things cannot get extremely ugly, but the time it takes will be stretched out.