Turkey is arguably one of the safest countries in the world to visit and the crime rate is low when compared to many Western European countries. Interpol ranks Turkey as the safest holiday destination in Europe for travelers.
For sure common sense precautions should be taken against petty crimes such as pick pocketing, bag snatching etc. but by and large visitors will find Turks to be friendly and helpful.
The following link may help you to compare the various crime statistics in Turkey against those in other countries.
http://www.nationmaster.com/graph/cri_tot_cri_percap-crime- total-crimes-per-capita
Turkey is number 54 on the list.