What are some quotes from Hamlet that question Hamlet's reasons for living?
Perhaps the most famous speech in English drama, and certainly in all of Shakespeare's plays, is Hamlet's "To be or not to be" soliloquy in Act 3, Scene 1. In this speech, Hamlet is literally asking whether it would be better to live or to die.
To be, or not to be, that is the question:
Whether 'tis nobler in the mind to suffer
The slings and arrows of outrageous fortune
Or to take arms against a sea of troubles,
And by opposing end them. To die, to sleep—
No more—and by a sleep to say we end
The heartache, and the thousand natural shocks
That flesh is heir to? 'Tis a consummation
Devoutly to be wish'd. To die, to sleep—
To sleep—perchance to dream. Ay, there's the rub! (III.i.63-72)
Hamlet has lost faith in marriage, and to some extent women in general (hence his mistreatment of Ophelia), as a result of his mother's quick marriage to Claudius. Hamlet grieves the loss of his father and laments his own apprehensions about avenging that death. Having lost faith in humanity and himself (his lack of action to avenge his father's death), he questions whether it would be better to end all his suffering by committing suicide. Hamlet reconsiders such a notion because he does not know what lies beyond death - "perchance to dream."
Later in this same soliloquy, Hamlet continues this reconsideration, thinking that death is a mystery which may be as, or more, undesirable as life.
But that the dread of something after death
The undiscover'd country, from whose bourn
No traveller returns, puzzles the will,
And makes us rather bear those ills we have
Than fly to others that we know not of? (III.i.85-89)
Hamlet thinks that the uncertainty of life after death is frightening enough to forget about suicide and face life's problems.
Hamlet concludes this soliloquy saying that this practice of considering and reconsidering the merits of life and death makes a coward of him because, rather than act (be it suicide or avenging his father), Hamlet spends too much of his time thinking about the philosophical implications of every decision. "Thus conscience does make cowards of us all" (III.ii.90). This is a recurring theme in the play: Hamlet's delay. Hamlet admonishes himself for this but continues to delay taking action because he's an intellectual and feels compelled to analyze the significance of every choice he is faced with: obviously including the most significant choice of life or death.