I can add a couple more examples. In Act 2, Hamlet's conversation with Rosencrantz and Guildenstern that begins with "What a piece of work is man," is an example of a speech that questions man's purpose in the world. In this speech Hamlet looks at the exquisitely formed human and questions the purpose of this "quintessence of dust."
In Act 4, Hamlet explores once more the purpose of human existence in his soliloquy beginning with "How all occasions do inform against me." Here he explores the purpose of action and how it justifies a man's life.
In Shakespeare's Hamlet, we find there are many quotations that reflect Hamlet's take on human existence: this is, after all, one of the major complexities of the play...Hamlet's ability to deal with the serious nature of life: his own, in connection with others.
Hamlet speaks of human existence in the "To be or not to be" speech.
To die—to sleep,
No more; and by a sleep to say we end
The heart-ache and the thousand natural shocks
That flesh is heir to: 'tis a consummation
Devoutly to be wish'd. (III, i, 5-9)
This quote speaks about death—maybe it's like sleeping, which would be easier than facing daily hardships...of being extremely tired of life's oppressions—is there a release after death? We are all moving to an unavoidable end—at times, fearful and at other times, sensing release.
Who would fardels bear,
To grunt and sweat under a weary life,
But that the dread of something after death,
The undiscovere'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, 21-27)
This part of the same speech describes the fear humans have of leaving what they know—though it be horrible—for something of which they know nothing. The dread of the unknown is common human reaction.
We find it once more in the following.
What a piece of work is a man, how noble in reason, how
infinite in faculties, in form and moving how express and
admirable, in action how like an angel, in apprehension how like
a god! the beauty of the world, the paragon of animals—and yet,
to me, what is this quintessence of dust? Man delights not me—
nor woman neither, though by your smiling you seem to say so. (II, ii, 303-308)
Here Hamlet speaks to the glorious creation of man—remarkable! And yet, he sees nothing that inspires him: he is disheartened. (He has Claudius, Gertrude, Polonius and perhaps Ophelia to thank for this.) A common theme regarding our view of life is avoiding cynicism in contemplation of the magnificence of man, or life, when people disillusion us.
What have you, my good friends, deserv'd at the hands of
Fortune, that she sends you to prison hither?
Prison, my lord?
Denmark's a prison.
Then is the world one.
A goodly one...Denmark being one o' th' worst...for there is nothing either good or / bad, but thinking makes it so. To me it is a prison.
This passage describes Hamlet's sense of feeling trapped, especially based on his father's challenge that Hamlet avenge the old King's death. He feels as if his world is a prison. We can probably relate his feelings to our own when we feel enslaved by the job, a relationship, politics, etc.
Also in this passage is the famous quote:
...for there is nothing either good or
bad, but thinking makes it so.
Here Hamlet touches on the a struggle within ourselves: what do I believe? The world is saying one thing: I feel another. Hamlet is saying what we also know: perception is everything. It is normal to experience self-doubt—to look for something that will convince us to follow our own path, to find our personal truth.
Hamlet spends a lot of time philosophizing about life; all of this shows his attempt to come to terms with his own experience in a world that has quickly become a threat and burden to him. He is confused, conflicted and searching. These quotations may help us to more closely identify with this sad young man, making this a timeless play.
If you look closely at Hamlet's soliloquys, you can find a lot of good material. In his "to be or not to be" speech, Hamlet examines the very nature of human existence. In his rather distraught state, he wonders why he would put up with all the difficulties of his life and not just end it, in the end perhaps backing away because he fears the "undiscovered country," and the uncertainty of whether life's difficulties will continue in the next life.
You may also look at his monologue after watching the performance of the players where he tries to figure out how the players can exhibit such powerful emotion while acting out old stories. He cannot even feel what he thinks he ought to feel about his father's death and everything else yet these players can shed real tears as they get into their roles.