Leave expensive items at home. Do not take pricey jewelry on board. If you do take something expensive keep it out of plain view in your room. Instead lock it in the safe when not in use. Use credit cards or traveler's checks and leave large amounts of cash at home.
Attend the lifeboat drills. They will be held the first day of the cruise and announced so all passengers are aware of when they are. The chances are slim you will need to use a lifeboat. However the time to learn is not in an emergency.
Stay in public areas. Do not wander into deserted parts of the ship. When going ashore travel with other people.
Lock your cabin door. Do not open your door to people you do not know. Cruise staff should be uniformed. Call the pursers office if you encounter any problems with someone trying to get you to open your cabin door.
Limit the alcohol. Drinking in excess can hinder your judgment. It can also make you less likely to be aware of your surroundings. Some individuals may be more inclined to fight or start conflicts when drinking in excess.
Keep on eye on your drinks in the ships nightclub. Do not leave it unattended. Also do not accept a drink from someone you don't know. As in any bar it is possible for someone to slip something in your drink.
Trust your instincts. You want to have a great vacation and not be paranoid. But you may feel something is not quite right. If you see something suspicious call security or the purser's office to express your concerns.