When you're in an unfamiliar place, it's easy to think that somehow different rules apply. And yet the reality is that most of the common sense things you'd do at home to avoid getting ripped off are exactly the same common sense things you should do when you're traveling! There are a few extra precautions you need to take, but it's not as different as you might think.
Firstly, you want to avoid being robbed. So that means don't be conspicuous! Having a wallet stuffed full of local currency is always a temptation to thieves, so use traveler's checks or credit cards most of the time, and avoid carrying large amounts of cash. Traveler's checks are usually better, because they can be replaced quickly if stolen. Leave your valuables at home, or at least locked in the hotel safe. Keep your important documents and the bulk of your money with you at all times, preferably tucked away under your clothing, not in a handbag or pockets.
Secondly, stay in well populated areas. At home you'd hardly go wandering off into the seedy parts of town that are badly lit, so why do it on holidays? Be very wary of anyone who stops in a car near you, and definitely don't walk to the car if they call you. Also be careful of anyone who stops you in the street, it's very easy to yank a handbag off your shoulder and either run or drive away. If you do find you've been robbed, you may find you're better off going to your hotel or local embassy rather than a police station - at least they'll probably speak your language.
If you're going out at night, stay in well-lit areas, preferably with a group of people. Know exactly where you're going and go straight there without dawdling. It might be worth spending a little extra and taking a taxi, rather than walking. And if you do find yourself in a bad situation, don't try to be a hero. You'll almost always come off second best.
Of course, being ripped off doesn't just mean being robbed on the streets. There are plenty of scams set up to rip off unwary tourists. One of the most common is tour offers that sound like amazingly good value. Make sure you read the fine print! Also, it's not uncommon that you ring up to book in for the special tour, only to be told that it's not available on the dates you want, but for extra you can book it on the day you prefer. Be wary of hidden extra fees, upgrade charges, and high-pressure sales tactics.
You might also find you've "won" a free night's accommodation at a local resort. Sounds great doesnt it, as long as you don't mind attending the timeshare or discount travel club presentation, with possible high-pressure sales tactics afterwards. Sometimes it's tempting, and you think you'll be strong, but you might find you're better off skipping the free accommodation and saving yourself the hassle.
While it's important to be cautious of yourself and your belongings, it's also not necessary to be so paranoid that something might happen that you forget to enjoy yourself. If you stay inconspicuous and don't appear to have lots of money, chances are you'll be left alone. The crime rates in most parts of the world aren't greatly different to the average big U.S. city, so as long as you use some common sense, you'll have a great holiday.