EU citizens can enter Greece for an unlimited length of time.
Non-EU citizens can stay in Greece for up to three months on production of a valid passport.

Citizens of the US, Canada, Australia and New Zealand can stay in Greece for up to three months on production of a valid passport. South African citizens can stay for up to two months on production of a valid passport. No visas are needed for these stays. If you wish to extend these timescales you must obtain a permit from the Aliens Bureau.

Greece has strict regulations about the import of drugs. All the obvious ones are illegal but also some seemingly beneficial drugs such as codeine or tranquilisers are also banned. Medicines prescribed by a doctor for personal use are permitted so if you take any drug on medical advice then make sure you always carry enough for your needs during the entire stay and keep it in its original container.

The Greek authorities are very concerned about the loss of antiquities and national treasures. Therefore, if you intend to buy an old piece, be it an icon or some statuary, always deal with a reputable dealer and make sure you keep your receipts. Genuine antiquities will need a permit. Exporting antiquities without a permit is a serious offense.

For citizens of non-EU countries, allowances for goods bought duty-free to be carried into Greece are as follows:
-200 cigarettes or 50 cigars or 250 grams of tobacco.
-1 litre of spirits or 4 litres of wine.
-250 ml of cologne or 50 ml of perfume.