If you shop with credit cards, remember to only carry those cards you will be using. Report any missing cards right away (credit card companies don't hold you responsible for charges once you report the card stolen...), check your credit card statements for accuracy and keep a separate record of your cards and the numbers to call when they are lost or stolen.
If you carry cash to shop, only carry what you need, keep it in a safe place, and don't flash it around.
Store your gifts in the trunk before you leave the place you bought them. Don't get to your next location and then put things in the trunk. Use the store/mall lockers to store things if you don't carry them between shops at a single location. Immediately remove packages from your trunk when you return home - and don't store gifts in the garage (the garage lock is usually your weakest...).
Schedule deliveries when you will be home or have them delivered to a trusted, stay-at-home neighbor. If you live in a multi-unit building, bring deliveries for your neighbors into a secured area.
Keep your home lighted and don't leave gifts in plain sight.
Then, there have been an increase in thefts of electronic devices such as I-phones and Droids. When you are out in public, keep alert to your surroundings, don't be focused on these devices. Usually they are stolen in a "grab and run" type of action - so staying aware of your surroundings reduces your chances of being targeted. In the cities, these items have been stolen by single individuals who were hanging around in groups usually in the evening or at night, often near shopping areas or bus stops. Report these thefts immediately.
Most thefts are crimes of opportunity - don't give someone the opportunity to do you wrong...