A good personal security tip is to always keep track of what is going on around you. Wearing earbuds or talking on the phone dramatically reduces a person's awareness and ability to react in dangerous situations. If you are traveling, give full information about your plans to friends and family to make sure that they can always reach you.
When you are in a crowded area, keep your phone, documents and wallet close to you, and check them often. Be extremely alert if somebody is pushing you or crowding you on purpose. Don't enter an elevator if there is another person in it and they look dangerous or make you feel uncomfortable. If there is no choice, stay close to the control panel so you can press the alarm button at any time.
When you enter a new building, familiarize yourself with escape routes. When walking, make sure that both of your hands are free and you are ready to protect yourself at any moment. Stay away from parked cars that have engines running or if there are people inside. Before using an ATM, look around to make sure that there is nobody watching you or waiting for you. Put away the money as soon as possible, and never show large amounts of money in public.