Be conscious of your surroundings. Always be alert and have a safety state of mind. Don't talk on your cellphone or wear headphones when you're in a parking lot. Be alert to what is going on around you. If you see someone suspicious, turn around and go back in the store.
Wear your purse over your shoulder. Wearing your purse over your shoulder makes it harder to grab because it's close to you. A purse worn across your body is much easier for someone to snatch. Also, take your keys out of your purse when you are going to your car. That way if someone does grab your bag, you'll still have your car and house keys and you can at least still drive away to safety.
Ask for help. If it's late and it's dark out, especially if you're alone, ask someone from the store to escort you to your car. Most stores are concerned about the safety of their customers and will send someone out with you.
Protect yourself with your shopping cart. Back in with your shopping cart when you open the driver's door. That way you have a built up a barrier on both sides of you.
Use your car antenna as a weapon. It's easy to yank if off. You could also use a windshield wiper.
Scream if you're attacked. Screaming is good because it attracts attention to your situation.
Keep a whistle with you. A whistle will attract more attention than screaming ever could.