During World War II, Greece was occupied by the Germans, as was most of Europe. Many of the Greek anti-German partisans, members of the underground resistance, were inspired and equipped by Soviet Communists. At the end of the war there was a strong Communist movement in Greece. Their reasoning went something like "we Reds fought and died for you when others did not, so we deserve the right to govern Greece."
It is interesting that in the U.S. we hear a lot about the Spanish Civil War between forces of left and right, but hear almost nothing about the post-World War II Greek Civil War where the two sides were the same. President Harry Truman put resources into Greece to prevent a Communist takeover. Greek Communists have never forgiven the U.S. for our help to their non-Communist enemies.
Although much of the rioting has been aimed at Germany's reluctance to subsidize fellow EU member Greece, some of it has been aimed at the U.S. Embassy. I suppose it doesn't help that Prime Minister George Papandreou, while the son and grandson of former Greek Prime Ministers, was born in the United States, and has both an American mother and American citizenship. He has to try to get Greeks to accept less from and give more to their government, never a happy prospect.