Negotiate a rate before you get in. Don't take unauthorized taxi cabs. Make sure the cab you use is licensed, and jot the license number down just in case. Cruise directors can tell you which are legal. Be aware of your surroundings.
Thieves look for easy prey.
Whenever possible, go ashore with a small group of passengers rather than on your own. Stick close to each other. Don't wander alone into unfamiliar areas. Ask the cruise director's staff about which areas of a port city to avoid. And try to avoid opening your wallet in crowded public places.