Ladies with purses should hold them by handles or straps instead of just draping them over a shoulder. Men should carry their wallets in a front pocket, rather than in a back pants or jacket pocket.
Never leave bags unattended.
Keep ATM cards separate from PIN codes. Memorize your PIN and keep it to yourself. Be aware of others that may be watching you at the ATM. If they see you enter your PIN and watch for the pocket where you keep your card, they can steal the card and drain your bank accounts much easier. Pick well-lit ATMs, and consider having a friend accompany you to get cash.
Be aware of your surroundings.
Watch out for people who are JUST watching other people! If you see someone acting suspiciously walk away.