Regarding Shakespeare's Hamlet, the play does fit the characteristics set forth by the Greeks, specifically Aristotle.
Greek tragedies there is hamartia which indicates that the protagonist has somehow "missed the mark," usually seen in his tragic flaw. In Hamlet, the Prince's tragic flaw is "indecision," in taking so long to exact revenge on Claudius for Old Hamlet's murder. Thinking of the players, Hamlet says:
O, what a rogue and peasant slave am I!
Is it not monstrous that this player here,
But in a fiction... (545)
Could force his soul so to his own conceit
That from her working all his visage wann'd,
Tears in his eyes, distraction in's aspect...
Yet I, (560)
...can say nothing! No, not for a king,
Upon whose property and most dear life
A damn'd defeat was made. Am I a coward? (565)
Why, what an ass am I! This is most brave,
That I, the son of a dear father murder'd,
Prompted to my revenge by heaven and hell,
Must, like a whore, unpack my heart with words (580)
And fall a-cursing like a very drab...
Another aspect of Greek tragedies is found with peripeteia—a reversal of circumstances in literature. Hamlet returns to the castle for his father's funeral, his family's happiness shattered, and he feels as if he is the only one that is mourning his father; he tells his mother that his grief is real:
Seems, madam? Nay, it is. I know not seems.
'tis not alone my inky cloak, good mother,(80)
Nor customary suits of solemn black,
Nor windy suspiration of forced breath,
No, nor the fruitful river in the eye,
Nor the dejected havior of the visage,
Together with all forms, modes, shapes of grief,(85)
That can denote me truly...I have that within which passeth show,
These but the trappings and the suits of woe.
Greek tragedies also have anagnorisis which is when the protagonist makes an enormous, life-altering discovery. We see this when the Ghost appears to Hamlet and tells him that Claudius murdered him. The Ghost says:
Now, Hamlet, hear.
'tis given out that, sleeping in mine orchard, (40)
A serpent stung me...But know, thou noble youth,
The serpent that did sting thy father's life
Now wears his crown.
Tragedy is defined as something terrible that happens to a story's hero. It could be death or a severe change in circumstances. The tragedy the hero or heroine experiences is due to pride ("hubris"), fate and decisions of "the gods." There is also difficulty when the hero tries to accomplish something important, but is unable to move forward due to some personal shortcoming or obstacle.