A recent paper by Aurthur J. O'Connor and Famecount looked at 30 top brands from June 2010 through June 2011, and found that number of Facebook fans was correlated with the stock price. Looking at the charts below, I can see how it's pretty significant. You can't see these graphs very well, but the vertical axes are price, the horizontal are Facebook fans.
In my 1994 dissertation I found that if I counted up stories in Nexus, these stories counts explained the relative ownership percentage of mutual funds in regressions that included price, size, and volatility. That is, in the context of these other variables, stocks more frequently in the new tended to have larger mutual fund ownership. One could imagine fund being both more aware of these companies, and having an easier time explaining their ownership in these companies.
Contemporaneous correlations are one thing, predictions another. Stocks with higher volatility generate more news than less volatile firms. Such stocks are then ‘in play’, and so become relevant to the investor interested in deviating from the index. Further, they create a default value, in that once everyone seemed to have internet stock in their portfolio, or some exposure to residential real estate, it seemed prudent to also have some, especially if one were indifferent. Given short constraints and overconfidence, this increased focus on volatile stocks leads to lower future returns. I imagine this might be interesting to look at whether this is more useful as a short-term momentum indicator, or a longer-term mean-reverting signal. The trick for the longer term predictability, is that you need a survivorship bias free data set with historical data going back several years, so I doubt that Facebook or Twitter have enough data to test anything with a horizon greater than 1-week.