Use a money belt. They come in all kinds of shapes and forms and are, in short, bloody brilliant. Keep it close to your body where strangers can't get hold of it. Keep your passport, plastic cards and most of your cash in your money belt when you're traveling.
Always keep a small amount of money in your pocket or in a light purse in your pocket - but never more than what you can afford to lose. It's like a decoy for thieves and as a bonus you can always pay for your minor purchases without having to flash your money belt.
The safest place for a traveler to keep his/her money is at the hotel. If the hotel doesn't have a safe, they may offer to keep your valuables safe in a sealed envelope at the reception. The second safest place is in your money belt. The third safest place is hidden in your luggage in your hotel room (but we strongly advise against that if you don't trust the staff). The fourth safest place is in an ordinary purse in your pocket, but please be aware that in this case you're treading dangerous waters. Our recommendation is not to bring valuables when traveling the world - and if you must bring those flashy diamonds for party and looking-good purposes, make sure they are fake and affordable to lose!
A lot of travelers experience theft and robbery during their traveling endeavors. But it only takes a little consideration to make a huge difference and play it safe.
But take it easy, there is no point in running around scared out of your wits during your entire trip. If you just use your head and don't do anything stupid, everything will be fine. Your travel insurance will eventually cover your loss.