To echo what most people say, the important thing when traveling is to use common sense. A lot of people who get into trouble were being naive or ridiculous, and they are the sorts who would have gotten into trouble back home. Don't go out drunk. Be watchful. Stay with crowds. Be trusting, but don't go overboard. You can be taken advantage of more ways than you think, and just because someone says something does not mean it is the truth. Really, it boils down to this: Be aware, be wise, and think before you act.
Also, I always say this because it can save lives, but post your itinerary on line or give it to the hotel front desk, just so someone knows where you last where in case anything happens.