What do traders use volatility for if they are not interested in the option space? Are there volatility patterns that can predicts future movements of asset prices?
Yes, when volatility goes up, it is a signal that asset prices are going to be more volatile. Seriously, that is a useful piece of information. If you want to take a certain amount of risk, you will need to reduce your positions.
If you measure volatility as the standard deviation of (rate of) returns, it is immensely important in a whole host of methods for financial analysis. It's primarily used as a measure of risk.
E.g., when doing portfolio optimization, in context of modern portfolio theory, this is taken to the next level where co-variance of each asset's rate of return is aggregated into a single portfolio variance. Remember that variance is simply the standard deviation squared, i.e., "volatility" squared. This is then combined with the expected return (mean of rates of return) of the portfolio, making it possible to optimize the allocation of your capital such that you get the lowest risk (i.e., volatility) given a required minimum return, or best return given a maximum level of risk (i.e., volatility). If you'd like to know more, I wrote about it in this blog post.
In the past volatility, as the standard deviation or returns, was also used a lot for value-at-risk calculations, but is now frowned upon as it assumes that returns are normally distributed. In essence you measure the standard deviation of the rate of returns, and use this statistically to say how much you stand to lose (or more) given a probability, say 5%. Example output of such an analysis would be: "With the proposed portfolio X, there is a 5% chance of losing more than 10% within the next month". Today you would use other methods, like Monte Carlo simulations, to get better VaR estimates.