William Shakespeare certainly took some of his ideas about what made a tragic hero from the Greeks before him, but he also added his own spin. The Greeks believed humans were ruled by fate, and this is highly evident in Greek mythology. In many myths, the characters consulted oracles, and were told what their fate would be. The rest of the story was often spent trying to change that fate, with no real hope of doing so. A perfect example is the myth "Oedipus Rex," where, out of ignorance of his own birth, Oedipus is told that he will kill his father and marry his mother. Oedipus leaves the couple he believes are his parents to change this terrible destiny, much later discovering they were actually his adoptive parents, and the story ends just as fate predicted.
Shakespeare's tragic heroes, however, are depicted as individuals responsible for their own destiny. Decisions they personally make lead to their downfall. Othello, for instance, misjudges several situations, and though evil forces abound, it is his own jealousy that causes his demise. To sum up, the Greek's vision was one of theo-centrism (the gods were at the center and controlled everything), where the Elizabethans of Shakespeare's time believed the individual's actions were primary.