Why are Greeks so leftist?

Good question! I trust someone more knowledgable will reply (who actually lives there now).

Of course, not all Greeks are leftist, and as with much of the West, the nominal left-wing parties have drifted further and further to the centre (Panhellenic Socialist Movement, PASOK). There are two related questions here: why has the Left been historically so strong in Greece in the 20th century; and why is Syriza so strong now?

Historical reasons include:

• the large number of dispossessed refugees from Asia Minor, and the ongoing low standard of living in the population until fairly recently;
• the lack of rule of law, which meant that people did not trust the government and were attracted to radical alternatives;
• repressive regimes for a large chunk of the 20th century;
• clientelism from the conservative governments (which was a problem right up until the Socialists took power, and ran their own clientelist state);
• left-wing alignment and advocacy from many of the musicians and authors of Greece. (Don’t underestimate the recruiting potential of Mikis Theodorakis back in the day.)

Elsewhere in the west, the mainstream left parties have drifted to the centre, and no further-left parties have taken their place. The Greens are doing well, but they have not overtaken the social-democrats. Greece is an exception, and that’s the second question: why is Greece the one country where the former Euro-Communists are  (nominally) running the show?

The answer of course is that Greece has been pushed to the wall in the past five years, and voters have lost all faith in the mainstream parties — the mainstream left more than the mainstream right, since the mainstream left is felt to have sold out on its principles, while the mainstream right hasn’t.
 
That’s why New Democracy (Greece) still exists, and has not been cannibalised by Popular Orthodox Rally (LAOS) or (shudder) Golden Dawn (political party). Not so for PASOK: in the past couple of decades, they have pretty much swapped percentages with SYRIZA, and have barely scraped in to parliament.