Greece is one of the most ancient of wine countries. While the ancient Greeks didn't really start wine-making as we know it (most likely pre-7,000 BC in the Caucasus/Mesopotamia region), they certainly pushed it forward and made it central to cultural development, and also gave the Romans a few ideas too.
Many grape varieties we use today can be traced back to Greece. In the modern era the country produces many styles of wine, some are very esoteric and ancient, and have been mostly drunk domestically (like Retsina). However, we are seeing more Greek wine out of Greece now and it is even becoming fashionable in some quarters. It really is a taste of antiquity, and there are so many styles to explore, away form the mainland, each island even has it's own wine heritage!