Greece is still one of the safest countries in the world but its not as safe as it used to be.
For a single woman traveling alone then its pretty safe if you take normal precautions. There are very few rapes in Greece.
There has been an increase in other kinds of crime however particularly Bank Robberies of which in Athens there are two a day on average. If you happen to be in the bank being robbed this kind of crime can affect you!
Some other types of crime however, like house breaking's needn't concern you as tourists, but hotel breaks, although rare, have been known to happen too. Pickpockets are another big thing to be aware of in Greece, especially on the trolley, bus or metro! Cell phones and wallets are a favorite theft item.
Times are changing, Greece is filled with immigrants legal and illegal's from all over the world; China, Iraq, Kurdistan, Turkey, Albania, Serbia, Bulgaria, Moldavia, Pakistan, Bangladesh, India and many more countries. The majority of these are hard workers looking to make a better life for themselves. A few of them are predators looking for a quick score.
Millions of tourists come here every year and have a great time so be aware in crowds, don't flaunt your wealth, dress and act conservatively and you ought to be fine. Don't act like a victim and odds are you wont be one!
x