I am a Greek-American and know that a good portion of Greeks loath Turks. I also know Greece was occupied by the Ottomans for 400+ years, which lead to the Greek war of Independence in 1821. But what specifically did the Ottomans/Turks do to the Greeks that would cause so much animosity to this day?
(I do know about the takeover of Northern Cyprus in the 70s that added fuel to the fire.)
Any discussion of historical memory is going to have to begin with how the memory was constructed, not with what actually happened in the past - that's where the previous person answering this question went wrong.
Whatever Ottoman rule was actually like, modern Greeks hate the Ottoman Empire because they are taught to hate the Ottomans in school, and this has resulted in anti-Ottoman sentiment permeating the consciousness of Greek people. When Greece gained independence its nationalist thinkers needed to justify the independence struggle and imbue it with deep meaning for the nation, so they latched on to the idea of the Ottomans as brutal oppressors and the Ottoman period as a dark age for Greece. That's not to say that no Greek ever experienced oppression while under Ottoman rule, but rather that for nationalist writers objective evaluation of the true condition of Greeks during the Ottoman period was not really important: it was self-evident to them that the Ottoman period had to have been a dark age, and everything they wrote was based on that assumption, with the goal of making the Ottomans seem as evil as possible.
From Kemal H. Karpat's article "Nationalism" in The Encyclopedia of the Ottoman Empire (2009).
The nationalism of the Balkan Orthodox Christians was also bolstered by the way these groups reconstructed their historical identities. Each national government in the Balkans wrote the history of its state from the perspective of the ethnic group in power. To foster national unity and gratify the national ego, historical events were sometimes distorted, magnified, or even falsified. Each nation described its pre-Ottoman existence as one of brilliant achievement and development that was ended by 500 years of “Turkish yoke.” This nationalist identity went hand-in-hand with the view that Turks—which in the vocabulary of post-Treaty of Berlin nationalism meant “Muslim,” particularly the Bosniaks and other converts to Islam—were interlopers or renegades and betrayers. The focus on ancestral “national” lands led the Balkan nation-states into conflict and wars unknown during those first Ottoman centuries now referred to as the Pax Ottomanica, or Ottoman peace. The disintegration of Yugoslavia, the Serbian attacks on Slovenia and Bosnia, the ethnic cleansing, and the Serbian-Croatian wars of 1991–95 stand as the saddest enduring results.