The most recognizable and widely available varietal is Assyrtiko. Stick with the wines from Santorini and Crete for the highest quality. Seek out Assyrtiko if you enjoy dry Riesling, Chablis, or dry Furmint. A few amazing producers: Hatzidakis, Economou, Sigalas, and Koutsagiannopoulos.
Xinomavro is considered by most to be the highest quality red grape. Stick to wines from Northern Greece, specifically the province of Macedonia. Seek out Xinomavro if you enjoy Nebbiolo and Pinot Noir. Naoussa Xinomavro is similar to Barolo but a little more rustic and Amyndaio Xinomavro is like Burgundy with more tannin. Several amazing producers: Thymiopoulos and Kir-Yianni for the most Barolo expression, and Alpha Estate Hedgehog Vineyard for the more Burgundian expression.
Malagousia is a white grape that was almost on the brink of extinction until the 80s and has exploded in popularity. Some of the best examples come from Thessaly. Seek these out if you enjoy Chenin Blanc from Saumur and Sauvignon Blanc from Sancerre. Look for Domaine Zafeirakis Microcosmos Malagousia. Alpha Estate makes a Malagousia that is very good.
Agiorgitiko is the highest quality red grape of the Peloponnese and the most widely planted and commercially important red grape after Xinomavro. The best examples are from high altitude sites in Nemea. It has some similar characteristics to Merlot, Garnatxa, and Mencia. Domaine Skouras makes some fantastic single varietal and blended Agiorgitiko and should be fairly easy to find. Their Nemea and Synoro cuvees are especially great.
Moschofilero is the most important white grape of the Peloponnese. To call it an aromatic grape is really an understatement. Mantinia is the highest quality appellation for Moschofilero and some of the best examples are the Domaine Skouras Salto cuvee and the more experimental wines made by Troupis.