Aztecs carried out human sacrifices to appease their gods. The Roman Catholic Church had the Inquisition, tortures, witch hunts, Galileo's trial, etc. Islam has the jihads. Many wars and other atrocities have been committed (and still are) in the name of religions. Since I am Greek, I have been given the impression that Orthodox Christians were always the good guys, the martyrs, the persecuted, the victims. Have there been any generally considered "crimes"/atrocities that are attributed to the Orthodox Church?
It is much harder to commit atrocities when you are out of power (not impossible, of course, but harder) The specifically Greek Orthodox Church was of course out of power from at least 1453 until 1821 or so. I tend not to think of "crimes" committed by institutions, especially things that weren't illegal back then, but among the "less than savory" things that Orthodox Church has been involved with, the first three that come to mind are:
Persecution of Old Believers in Russia, with some old believers being murdered, many more facing persecution, and thousands fleeing Russia for Siberia or the New World. I am no expert in this but, while murderous, this is less murderous than a lot of religious persecutions. Also, many Russian and Ukrainian Orthodox clerics supported violent antisemitism, compared to Western Europe, the Orthodox Churches were more mixed in their treatment of Jews.
The support of the Church for the 1967 military coup and subsequent nondemocratic governments. While it was clearly not led by the Church, the Church had a close relationship with the juntas. Important slogans from this period include "Greece for Christian Greeks" and "Religion, Family, Tradition". Though it's worth noting that shortly after the coup, the military made Archbishop Chrysostomos II resign and replaced him with Archbishop Ieronymos I, who was more coup friendly.
Some have implicated the Serbian Orthodox church for its role in the violence and ethnic cleansings that characterized the break up of Yugoslavia. See here, for example.
If one considers it to be the continuation of early Christianity ...
... then the persecution of the Hellenic religion (the 'pagan' worship of the Olympian Pantheon) encouraged by early Christian Roman emperors, leading to the destruction of Hellenic temples, statues and artefacts ... and to the murders of Hellenic philosophers and/or priests by Christian mobs (the lynching of Hypatia for example) ...
... could conceivably be blamed on 'the Orthodox Catholic Church'.