Are Stock Market Prices Random?

"The math works. Over the course of a season, there's some predictability to baseball. When you play 162 games, you eliminate a lot of random outcomes. There's so much data that you can predict: individual players' performances and also the odds that certain strategies will pay off."
-- Billy Beane

Though asked in many different ways, this one question is definitely a contender for most frequently asked question... are stock market prices random?  The jury is now (as ever) still out, but for my 2 cents, the unequivocal answer is...