First: do you understand why it dropped? Was it overvalued before, or is this an overreaction to some piece of news about them, or about their industry, or...? Arguably, if you can't answer that, you aren't paying enough attention to have been betting on that individual stock.
Assuming you do understand why this price swing occurred -- or if you're convinced you know better than the folks who sold at that price -- do you believe the stock will recover a significant part of its value any time soon, or at least show a nice rate of growth from where it is now? If so, you might want to hold onto it, risking further losses against the chance of recovering part or all of what is -- at this moment -- only a loss on paper. Basically: if, having just seen it drop, you'd still consider buying it at the new price you should "buy it from yourself" and go on from here. That way at least you aren't doing exactly what you hope to avoid, buying high and selling low. Heck, if you really believe in the stock, you could see this as a buying opportunity...
On the other hand, if you do not believe you would buy it now at its new price, and if you see an alternative which will grow more rapidly, you should take your losses and move your money to that other stock. Or split the difference if you aren't sure which is better but can figure out approximately how unsure you are.
The question is how you move on from here, more than how you got here. What happened happened. What do you think will happen next, and how much are you willing to bet on it?
On the gripping hand: This is part of how the market operates. Risk and potential reward tend to be pretty closely tied to each other. You can reduce risk by diversifying across multiple investments so no one company/sector/market can hurt you too badly --- and almost anyone sane will tell you that you should diversify -- but that means giving up some of the chance for big winnings too. You probably want to be cautious with most of your money and go for the longer odds only with a small portion that you can afford to lose on.
If this is really stressing you out, you may not want to play with individual stocks. Mutual funds have some volatility too, but they're inherently diversified to a greater or lesser extent. They will rarely delight you, but they won't usually slap you this way either.