No-one knows exactly how many organisations and individuals use ANNs to predict stock market prices as people tend to be secretive about their methods. One of the postulates of the Efficient Market Hypothesis is that information flows efficiently round stock markets and so any ANN that had a high success rate would, if made public knowledge, be quickly adopted by others. Essentially, this begs the question: Why spoil a good thing by making it generally available?
So perhaps the perfect neural network, that can predict every twist and turn in the market, is out there. If so, the chances are that you and I will never get to hear about it!