Greece is one of the safer places in which to travel, with crimes against persons (especially foreigners) exceedingly rare; when it does happen the perpetrators are often other foreigners. The Greeks’ reputation for honesty certainly contributes to the country’s popularity among tourists. In the larger towns there are burglary rings, but this will probably not concern you – even car break-ins are not the norm.
In the hills and remote islands, problems are virtually unheard of, though some of the northerners will attempt to scare you with one-third-true stories of hungry Albanian refugees brandishing sharpened spoons, lying in ambush in the forest. The main culprits here are four-footed, not two-footed, food thieves, field mice especially. Always secure your belongings in a beast-proof fashion before turning in for the night.