Blend in: Forget the khaki cargo pants and photographer vests. Don't dress like a tourist. Similarly, don't wear ostentatious designer clothing.
Keep the fancy DSLR camera tucked away... in a plain-looking bag instead of a brand-emblazoned camera bag, and only take it out for the shot - then put it away.
Ditch the backpack and fanny pack: They scream "I'm a tourist, rob me!"
If you do carry a bag, don't put anything valuable in it: No cards, cash, passports or expensive music players. If a thief tries to snatch it you'll know there's nothing of value in there and it's easy to let it go.
Get a travel credit or debit card... and keep a low balance in it (top it up online from your other account when needed). If you lose the card, or it gets skimmed, or you are subject to an express kidnap, the thieves won't get your entire life savings.
Don't walk alone, especially at night: Don't walk down quiet, deserted back streets - keep to the busy thoroughfares.
Buses are okay to use during the day, but take a taxi at night: Call a registered radio cab company. If anything bad does happen, give your antagonist what they're after, don't struggle or scream
Ensure you have the appropriate emergency numbers... and your travel insurance policy details on hand. Either written down or with Tripwise, TID's free app for iPhone and Android. Always report incidents or issues as soon as they arise.