What comparisons can be made between Hamlet and Death of a Salesman?
One similarity between Shakespeare's Hamlet and Miller's Death of a Salesman is the theme of Appearances vs. Reality.
The enotes Study Guide on Miller's work says the following:
Appearances vs. Reality
What appears to be true to the characters in Death of a Salesmen is often a far cry from reality, and this is communicated numerous times throughout the play. Willy's frequent flashbacks to past events—many of which are completely or partly fabricated—demonstrate that he is having difficulty distinguishing between what is real and what he wishes were real. Willy's imagined conversations with his dead brother, Ben, also demonstrate his fragile grip on reality. Willy's mind is full of delusions about his own abilities and accomplishments and the abilities and accomplishments of his sons. Biff and Happy share their father's tendency to concoct grand schemes for themselves and think of themselves as superior to others without any real evidence that the schemes will work or that they are, indeed, superior. At the end of the play, each son responds differently to the reality of his father's suicide. Biff, it appears, comes to the sad realization that his father "didn't know who he was," and how his father's unrealistic dreams led him away from the satisfaction he could have found if he had pursued a goal that reflected his talents, such as a career in carpentry. Happy, who had previously given the appearance of being more well-grounded in reality but still hoping for something better, completely falls into his father's thought pattern, pledging to achieve the dream that his father failed to achieve.
This coincides with the theme of "seeming" in Hamlet. Hamlet introduces the theme himself when his mother asks him why he still seems so sad about his father's death and he replies:
"Seems," madam? Nay, it is. I know not "seems."
'Tis not alone my inky cloak, good mother,
Nor customary suits of solemn black,
Nor windy suspiration of forced breath,
No, nor the fruitful river in the eye,...
for they are actions that a man might play.
But I have that within which passeth show,
These but the trappings and the suits of woe. (Act 1.2.76-86)
And people or situations seem to be one thing, and are actually the opposite, the rest of the play.
Hamlet seems mad, but probably is not. Ophelia seems sincere, but she is really spying for her father and Claudius. Ros. and Guild. seem to be Hamlet's friends, but they spy on him, too. Gertrude seemed to love King Hamlet, according to Hamlet, but marries Claudius soon after the king dies. Laertes seems the better swordsman, but Hamlet wins the duel.
The contrasts between these two plays are more frequent than the similarities, but this similarity does exist--they both reveal the theme of appearances vs. reality.
Another point of comparison between the two works can be the focus on two generations: how the actions and decisions of the previous generation affect the younger generation. In Death of a Salesman, you might focus on Willy's effect on Biff and Happy. His ideas of success have been transferred to the sons, who fail in their attempts to actualize these ideas. With Hamlet, you could focus either on the Ghost or on Claudius. Claudius would perhaps be the better choice. His corruption pervades the court, just as Willy's dreams and infidelity corrupt his house, and Hamlet, like Biff, knows the truth. But both young men are tainted by their elders. Hamlet in seeking vengeance against Claudius becomes ruthless and cold; Biff at 30 still has not found himself.
Both plays also have foils that you might also explore. Bernard is Biff's foil. Bernard is "liked, but not well liked" and becomes quite successful as a lawyer. Bernard becomes the success that Willy would have wanted for Biff. Fortinbras is Hamlet's foil. He is at first thwarted in his attempt to regain his father's lands but in the end he is the winner of all of Denmark. He takes the kind of action that Hamlet admires.