Leave precious jewelry at home, along with other valuables that you don't need to have with you. Don't bring anything you can't bear to lose.
Pack as light as possible. It's much easier to keep an eye on your stuff when you're carrying only one bag.
Make an effort to fit in. The less you look like a tourist, the less likely you'll be targeted.
Make copies of all important documents before you leave home, including passport and traveler's checks. Leave one copy at home with someone you trust, and bring the other copy with you, stored separately from the documents.
Wear a money belt or pin your valuables into inside pockets of your clothing.
Split up your valuables. Keep cash safely pinned into an inside pocket, credit cards in a different pocket or money belt, and so on. If something does happen, you stand a good chance of keeping at least some of your valuables.
Watch out for "tag-team" and distraction tactics, in which one member of a team spills something on you or asks for directions, while the other steals your wallet or cuts your purse straps. Be aware of the people around you and follow your instincts.
Stay in well-populated, well-lit areas. Don't take shortcuts down alleys, and don't walk alone at night. Talk to the locals about safety - ask them which areas they avoid and which areas become dangerous after dark.
Carry as little cash as possible. Change traveler's checks as you need to, and never pull a wad of cash out of your purse or wallet to pay for anything.
Avoid getting into confrontations with would-be muggers or thieves; your safety is more important than your money. Report problems to local police.