If anything is God-given to the Greeks, it is their climate. The best time to visit most of Greece is outside the mid-July to end of August peak season, when soaring temperatures, plus crowds of foreigners and locals alike, can be overpowering.
You won’t miss out on warm weather if you come in June or September, excellent times almost everywhere but particularly on the islands. An exception to this, however, is the north mainland coast – notably the Halkidhikí peninsula – and the islands of Samothráki and Thássos, which only really bloom during July and August. In October you will almost certainly hit a stormy spell, especially in western Greece or in the mountains, but for most of that month the “little summer of Áyios Dhimítrios” (the Greek equivalent of Indian summer) prevails, and the southerly Dodecanese and Crete are extremely pleasant. Autumn in general is beautiful; the light is softer, the sea often balmier than the air and the colours subtler.
December to March are the coldest and least reliably sunny months, though even then there are many crystal-clear, fine days. The more northerly latitudes and high altitudes endure far colder and wetter conditions, with the mountains themselves under snow from November to May. The mildest winter climate is found on Rhodes, or in the southeastern parts of Crete. As spring slowly warms up, April is still uncertain, though superb for wild flowers, green landscapes and photography; by May the weather is more settled and predictable, and Crete, the Peloponnese, the Ionian islands and the Cyclades are perhaps at their best, even if the sea is still a little cool for swimming.
Other factors that affect timing for Greek travels have to do with the level of tourism and the amenities provided. Service standards occasionally slip under peak season pressure and room prices on the islands can rocket. If you can only visit during midsummer, it is wise to reserve a package well in advance, buy any ferry tickets beforehand or plan your itinerary off the beaten track. You might choose, for instance, to explore the less obvious parts of the Peloponnese and the northern mainland, or island-hop with an eye for the remoter places.
Out of season on the islands you will have to contend with reduced ferry and plane services plus fairly skeletal facilities when you arrive. You will, however, find reasonable service on main routes and at least one hotel and taverna open in the port or main town of all but the tiniest isles. On the mainland, winter travel poses no special difficulties except, of course, in mountain villages either cut off by snow or (at weekends especially) monopolized by avid Greek skiers.