Hamlet is locked into this hateful place of Denmark; he is trapped by what he must do (kill the king) and he cannot leave. Snape can be said to have the same type of connection with his past. He must (for some reason we don't know yet) redeem himself by delving into matters which he probably want to avoid. I get the idea he just wants to block out his Death Eater behavior and live. But like the spectre of the King which haunts Denmark, so too does Snape's past, and he must put it to rest.

It is interesting to note that Hamlet is talking about an actor who just gave a passionate speech from a play, and who was so emotional in performance. Hamlet beforehand thinks if the actor really wanted to kill the king, he would be wonderful in the part. Really this is a discussion in modivation, in acting, which Snape does a lot .

Hamlet here admonishes himself for his inaction. He's been dilly-dallying around like a daydreamer, talking about his feelings but not doing anything. Sometimes I see Snape contemplating his inability to act, maybe due to the fact he turned to Dumbledore's side. But this is more supposition than anything.

HAMLET:
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 wished. To die, to sleep --
To sleep, perchance to dream. Ay, there's the rub,
For in that sleep of death what dreams may come,
When we have shuffled off this mortal coil,
Must give us pause. There's the respect
That makes calamity of so long life.
For who would bear the whips and scorns of time,
Th' oppressor's wrong, the proud man's contumely,
The pangs of despised love, the law's delay,
The insolence of office, and the spurns
That patient merit of th' unworthy takes,
When he himself might his quietus make
With a bare bodkin? Who would fardels bear,
To grunt and sweat under a weary life,
But that the dread of something after death,
The undiscovered country from whose bourne
No traveler returns, puzzles the will
And makes us rather bear those ills we have
Than fly to others that we know not of?
Thus conscience does make cowards of us all,
And thus the native hue of resolution
Is sicklied o'er with the pale cast of thought,
And enerprises of great pitch and moment
With this regard their currents turn awry
And lose the name of action. Act 3, Scene 1, lines 64 to 95

I would not be surprised at all if Snape had thoughts of suicide. I am not alone in this--I have seen many fics which have him considering death over the trials and tribulations of his life. He, like Hamlet, has suffered over the idiocies of the world, from 'th' oppressor's wrong' and 'the law's delay' and especially the 'spurns that patient merit of th' unworthy takes'. Really, if Snape was an actor, then I would love to see him give this monologue.

I would not be surprised also if he fights with himself, and if he thinks "thus conscience does make cowards of us all". for he is cursed with the intelligent man's sensitivity, and his tendency to reason everything out could leave him at such a point.

This acknowledges the concept of fate, and that despite all we think, sometimes it just doesn't happen. Within Hamlet, this scene runs parallel to the famous 'To Be' speech. It is possible that Snape is a product of fate -- if he was not humilated at school, if he had not suffered from isolationalism, if certain events had not happened--then he would not be in this situation. Because Snape shows enough animostity in school to suggest he isn't enjoying his time at Hogwarts -- and we can guess by that assessment that he is not teaching to spread knowledge.Whether he cognatively ponders this point we might never know.

During Hamlet, a troupe of actors come to the castle and play "The Mousetrap". The story closely reflects what happened to Hamlet, mainly the murder of his father and the quick marriage of his mother. I just like this quote because it details the power of potions to 'bewitch the mind' and 'ensnare the senses'.

At this point, Hamlet is admonishing two childhood friends, Rosencrantz and Gildenstern, for taking him a fool. This is very reminsent to when Snape chews out Quirrell in the first book. Also when Potter tries to obviously lie to Snape regarding some of his behavior (Snape's Grudge chapter in PoA and when he threatens Potter with Veritserum comes to mind).

More of the above. (Though I doubt that anyone has called Snape 'sweet').

In the play, Hamlet has just killed Polonius, one of King Claudius's advisors. He is telling his mother that he is willing to put up with the consequenses of this murder,for he is working for a 'greater good'--that is, the revenge of his father. I get this feel from Snape, specifically from the third book--he is mean to his students only because he wants them to learn, to grow somewhat from the experience. Because probably, what his students experience is nothing compared to a government under Voldemort, full of corruption and tyrrany. One could say he is taking the lesser of two evils.

I think this is Snape's philosophy. We are thinking creatures, superior to animals in that respect. He also acknowledges sometimes how thinking can lead to indeciciveness, inaction as one ponders an issue. Here Hamlet admonishes himself for not acting. Perhaps the closest Snape comes to this is in the 5th book, when he is quiet while thinking about whether to tell Potter about what's really going on with Voldemort. I don't know if he belittles himself to the effect that Hamlet does, though. But we still have two books to go........