Well folks I want to tell you that Greece is one of the safest countries in the world and I will but I have to also mention that its not as safe as it used to be. There are PICKPOCKETS on the trolley and the metro!
If you are 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. Some, like house breaking's needn't concern you, 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! See my luggage suggestions for a few ways to foil the pickpockets. Cell phones are a favorite theft item too.
All in all Greece is safe but there are cases of people just disappearing too, unexplained cases of children missing and even adults. I am not going to point the finger at anybody in particular like the Nigerian drug dealers or the Gypsy pickpockets and pimps or even your garden variety Albanian hoodlum because the people that attempted to rob the National Bank of Greece in Jan 2006 were Greek. At least that one guy they shot was Greek! There were bullets flying all over the place too! Big city bank robbery is one of the most common crimes in Greece so just hope you aren't in a bank when that happens.
Times are changing, Greece is filled with immigrants legal and illegal 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.