While travelling in Greece, keep some cash handy as not all places will accept cards. Especially while travelling to islands, make sure you carry only cash.
If you are planning to self-drive in Greece, make sure you have your list of travel documents and an international driving license.
If you are a single male traveller, proceed with caution. Some scams involving over-friendly locals, astronomical bills at the end of the night and sometimes, even roughhousing by thugs have been reported in the past.
Strictly obey signs that prohibit photography. Violations are dealt with with a swift and serious law.
Consumption of drugs and narcotics is strictly banned in Greece and amongst all European countries, it is the one where you will be punished by law for such an offence. The Greek law makes no difference between possession, consumption or usage and thus,even having small quantities on you can land you in trouble.
Smuggling or exporting any antiques from Greece is frowned upon and may even garner international media attention and an arrest.