This is certainly true in Greece, especially ion the larger cities and tourist areas (Athens, Mykonos and Santorini, etc).
Here are some tips to help protect yourself from being pickpocketed or mugged in Greece:
1. Go in larger groups (not by yourself) in areas that have nightclubs and bars in the early mornings (when clubs let out it is morning).
2. If you carry a bag or purse, make sure to have the strap around your body with bag in front of you (not in your back) and make sure the bag does not have very small straps that can be cut.
3. Keep your nice jewelry or watches at the hotel locked up when going shopping with massive crowds of tourists.
4. Always keep your cash and credit cards separate (I recommend putting some catch in your sock or shoe).
5. When you shop don't take out tons of cash to not make it visible, only the money to pay for what you are buying (if cash or use credit cards).
I am sure there are plenty of other ways to protect yourself from being pickpocketed in Greece, but these are some of the big things that come to mind!
Thanks for the great question!!