the possible betrayal of his mother. Hamlet isn't sure thatGertrude isn't involved in his father's death. After he stabs Polonius, thinking it's Claudius, he tells Gertrude that this bloody deed is almost as bad as "kill[ing] a king and marry[ing] his brother" (3.4.30). Gertrude denies such involvement, but it isn't clear whether Hamlet's fears are completely unfounded.

Ophelia is used as a pawn by her brother and father in order to gain information about Hamlet's motives and mental state. Hamlet has recently been involved in a relationship with her, and he seemingly truly loved her. Yet in Ophelia, he finds one more person whom he can no longer trust. Ophelia finds herself to be the subject of a great deal of wrath that comes from these feelings of betrayal, and Hamlet scoffs that "God has given [her] one face and [she] make[s] [herself] another" (3.1.143). The "face" in this line becomes a metaphor for Ophelia's personality or loyalty.

Rosencrantz and Guildenstern, two of Hamlet's old friends, also show up at the castle for a "friendly" visit. Hamlet is at first glad to see them, but his feelings quickly change when they won't honestly tell him why they are there. Hamlet asks them several times to be forthright about the purpose of their visit. They refuse. Hamlet asks them to be "direct" with him and proclaims, "If you love me, / hold not off" (2.2.300–301). This finally elicits a more truthful, though guarded, response from his old friends, but Hamlet realizes that they have already committed themselves to the loyalty of Claudius.

At every turn, Hamlet finds that he has been betrayed by people whom he once loved. This creates great internal conflict, which makes it difficult for Hamlet to trust anyone as he tries to discern the truth about Claudius.

Hamlet is a very complicated young man, emotionally and intellectually. A multifaceted individual, Hamlet is a man of many parts, so it's hardly surprising that he should be riven by internal conflicts of one sort or another.

The biggest internal conflict with which he must deal concerns his avowed aim to take revenge on Claudius, his wicked stepfather/uncle. Hamlet makes this vow right after the ghost of his father tells him that it was Claudius who murdered him while he slept in the garden one day.

And yet, as just about everyone who knows anything about Hamlet knows, the title character procrastinates. Instead of dashing off and running Claudius through with a sword, he hesitates, unable to do what he knows needs to be done.

Essentially, Hamlet is torn between his duties as a son and as a Christian prince. This helps to explain why he doesn't strike down Claudius while he's at prayer, even though it would be the easiest thing in the world to do. Hamlet is enough of a Christian to believe that Claudius might go to heaven if he's killed while praying, and that's the very last thing that he wants.

But cleaving to the ideal of what a Christian prince should be comes at the cost of inaction, so Hamlet is unable to settle his score with Claudius in a timely manner.

One internal conflict is his seeming fear of action; this results from his confusion over expectations of the Ghost and expectations of his religion.  He wants to avenge his father's death, but questions whether or not the Ghost is truly his father.  Because of this question and his religious beliefs, he suffers from inaction, from his failure to make a move.  He eventually compares himself to Fortinbras who can make a decision and act almost instantly, and this causes him considerable distress. 

He is also struggling internally with his love for his mother.  On the one hand, he truly loves his mother; on the other, he despises her for marrying her husband's brother and so soon after his father's death.  Her actions condemn her in the eyes of their Church and doom her in Hamlet's eyes

He is also having trouble dealing with Ophelia's betrayal.  Again, he loves her but is disgusted by her behavior: her trickery in refusing to keep his tokens of affection and her unwillingness to be honest with him reveal her betrayal.  For all of this, he reacts violently and cruelly, only to find out later that he has made a grave mistake. 

In all, Hamlet is suffering internally.  His father, mother, uncle, and lover have all caused him to doubt his own decision making, and for this he is thrown into terrible fits of internal depression.  

Hamlet appears to struggle with a sense of self-doubt. This is seen in his struggle with acting on his plot of revenge. Hamlet has vowed to avenge his father's murder, but for much of the play he does not act on it. This causes him to struggle with himself. At times, he curses his inability to act. Hamlet is more of a philosopher than an action oriented man, he tends to think things through and wonder at what motivates action than actually going through with something.

Hamlet seems to struggle with depression, as well. His thoughts on the people in his life, and life itself, are often dark and negative(although-rightly so at times!).

There are two major kinds of conflict: internal and external. Internal conflict is the struggle that one goes through inside. External conflict includes a struggle with another person, with nature, with God (or the "supernatural"), or with society. Hamlet faces almost all of these conflicts.

The one that is perhaps most central to Shakespeare's Hamlet is Hamlet's struggle within himself about whether the ghost that appears to him is really his father or a spirit sent from the devil. Hamlet tells the others that see the ghost that it is "honest," but he spends the rest of the play looking for proof to support what the ghost has said: that Claudius killed Hamlet's father. This is an internal struggle for Hamlet because he knows that it is a mortal sin to kill a king. If Claudius is innocent and Hamlet kills him, Hamlet will forfeit his eternal soul. After a great deal of skullduggery and the pretense of insanity, Hamlet devises a plan to prove Claudius' guilt by adding a scene to a play very similar to the murder of Old Hamlet:

…the play's the thing


Wherein I'll catch the conscience of the King. (II.ii.604-605)

Hamlet also experiences the conflict of man vs. man. Treachery in Denmark's royal court abounds, found in the snooping of Polonius; Ophelia's forced cooperation by the King and her father to spy on Hamlet; the willingness of Rosencrantz and Guildenstern to betray Hamlet in order to ingratiate themselves with the King; and, Laertes burning desire to kill Hamlet when the prince mistakenly kills Polonius.

Man vs. the supernatural appears in several instances: is the Ghost real or an apparition sent by the devil? Hamlet also bemoans the fact that God has declared that suicide a sin:

O, that this too too solid flesh would melt,

Thaw and resolve itself into a dew! 


Or that the Everlasting had not fix'd


His canon 'gainst self-slaughter! O God! God! (I.ii.132-135)

We might argue that Hamlet faces conflict with society: his uncle is chosen to be King over Hamlet—though Hamlet seems more concerned about his uncle's embarrassing carousing and his mother's "o'erhasty" remarriage to his uncle. 

The worst example of man vs. man that Hamlet experiences is Claudius' repeated attempts to have Hamlet killed. First he sends Hamlet to England with Rosencrantz and Guildenstern who hold letters that call for the King of England's aid in executing Hamlet. The King addresses the English monarch:

...thou mayst not coldly set

Our sovereign process, which imports at full,

By letters congruing to that effect,

The present death of Hamlet. Do it, England... (IV.iii.66-69)

Claudius also convinces Laertes (devastated first by his father's murder, and later by Ophelia's loss—which he also blames on Hamlet), to take part in a plot to murder Hamlet. Forgetting his honor, Laertes allows himself to be manipulated into engaging in a "friendly" duel in which Laertes will poison Hamlet (who unknowingly poisons Laertes as well). Claudius also tries to get Hamlet to drink poisoned wine, which Gertrude mistakenly drinks. In trying to hold onto the crown for which he murdered his brother, Claudius succeeds in poisoning Hamlet (and Gertrude), but Hamlet turns the King's treachery back upon him before Hamlet succumbs to his injury at Laertes' hand.

Hamlet's promise to avenge his father's death, obtaining justice for his murder, ends in Hamlet's death—the result of a multitude of conflicts in the play.

I would like to answer this question by approaching it from a slightly different angle. I think it is easy to jump to thinking of the conflicts that Hamlet as a character faces, and clearly there are many that he has to confront. However, this temptation to jump to the title character can lead us to forget and ignore the other important characters and the conflicts that they themselves face.

For example, let us think of Ophelia and the many conflicts that she faces. She is clearly in love with Hamlet, yet both her brother and her father command her to have nothing to do with him:

I would not, in plain terms, from this time forth,

Have you so slander any moment leisure,

As to give words or talk with the Lord hamlet:

Look to't, I charge you; come your ways.

This clearly presents a massive internal conflict for her, as she must choose parental obedience over the desires of her own heart. Then, having been commanded to stay away from Hamlet, she is then commanded again by her father to act as bait whilst Claudius and he eavesdrop on her conversation with Hamlet. Again, she must choose between loyalty to her lover and loyalty to her father. Lastly, when Hamlet kills her father, we can see the immense mental agony this must have caused her, perhaps explaining why she goes insane.

Likewise, let us remember that Laertes faces a parallel situation to Hamlet. He, like Hamlet, has had his father killed through foul means, and he, like Hamlet wants to avenge his father's death. Yet he faces an internal conflict as to whether to do this through treachery, as Claudius is suggesting, or through an honest duel. Lastly, he confesses all, perhaps signifying the resolution of this conflict, as he opts for honesty.

You might find it interesting to examine other characters and the various conflicts that they have and seeing what light they cast on the play rather than considering Hamlet alone. For example, think of Rosencrantz and Guildenstern, Gertrude, and even Claudius and the conflicts that they face. Good luck!

Hamlet's inner conflict centers around whether or not he should enact revenge upon his father's murder, or not.  Wrapped up in that conflict are questions about whether the ghost of his father was real or not, because if not, then he would be murdering his uncle all because an evil ghost prompted him to.  Also, Hamlet wonders whether or not he is capable of murdering his uncle; he spends so much of his time worrying and fretting about it, and so little time actually doing anything that he gets mad at himself for inactivity.  It takes Hamlet the entire course of the play to go from a man who is fearful and hesitant and wallowing about "in words" to a man who can stand up and declare, "the readiness is all."

Before he learns of his uncle's betrayal and murder of his father, Hamlet's inner turmoil was caused by his distaste of his mother's actions in marrying so soon after becoming a widow.  This conflict within him makes him so upset that he declares Denmark and everything in it "rotten" and vile.  He is grieving for his father while at the same time seething over his mother's quick recovery and marriage.   Once his father's ghost visits him, that conflict soon turns towards his own struggle to enact revenge.  I hope those thoughts helped; good luck!

In William Shakespeare's Hamlet, the greatest challenge that Hamlet must overcome throughout the play is his own indecisiveness.

Hamlet suffers from what is known in modern terms as "paralysis by analysis." Hamlet refuses to make a decision or act on that decision until he has thoroughly analyzed the situation. Since Hamlet is never satisfied that he's analyzed every possible aspect of a given situation, he's continually paralyzed by indecision.

Hamlet's father comes from the grave to tell him that he was murdered by his brother, Hamlet's uncle Claudius. Despite swearing to Heaven, Earth, and Hell to avenge his father's death, Hamlet hesitates to take any action because he wants to be sure that his father's ghost was telling the truth.

HAMLET. The spirit that I have seen
May be a devil; and the devil hath power
T' assume a pleasing shape; yea, and perhaps
Out of my weakness and my melancholy,
As he is very potent with such spirits,
Abuses me to damn me. I'll have grounds
More relative than this. (2.2.593-599)

Hamlet arranges for a play to be performed at court that recreates his father's murder, and he hopes to "catch the conscience of the king" (2.2.600). In other words, Hamlet hopes to catch the King acting guilty.

Even when Hamlet does catch the king acting guilty, which proves to him that the ghost was telling the truth—"I'll take the ghost's word for a thousand pound" (3.2.275-276)—Hamlet still does nothing.

In act 3, scene 3 , Hamlet has an opportunity to kill Claudius while Claudius is kneeling in prayer. Hamlet is standing over Claudius with his sword in hand, but Hamlet hesitates, in order to give himself time to think about the situation. Hamlet talks himself out of killing Claudius, and tells himself that he's going to wait for a better opportunity to kill Claudius.

HAMLET. ... When he is drunk asleep; or in his rage;
Or in the incestuous pleasure of his bed;
At game, a-swearing, or about some act
That has no relish of salvation in't
Then trip him... (3.3.91-95)

Hamlet envies Fortinbras for his ability to make quick decisions, even frivolous ones, and to put those decisions directly into action. A captain of Fortinbras's army says to Hamlet, “We go to gain a little patch of ground / That hath in it no profit but the name” (4.4. 18-9).

HAMLET. Witness this army, of such mass and charge,
Led by a delicate and tender prince,(50)
Whose spirit with divine ambition puff'd,
Makes mouths at the invisible event,
Exposing what is mortal and unsure
To all that fortune, death, and danger dare,
Even for an eggshell. Rightly to be great(55)
Is not to stir without great argument,
But greatly to find quarrel in a straw
When honour's at the stake. (4.4.49-58)

Hamlet's single spontaneous act in the play, when he killed Polonius when Polonius was eavesdropping on Hamlet's conversation with his mother in act 3, scene 4, occurs far too late in the play to have served as a lesson to Hamlet to avoid making hasty decisions or acting impulsively.

Nevertheless, Hamlet's accidental killing of Polonius represents Hamlet's behavior throughout the play. Hamlet doesn't act. He only reacts. Every substantive action that Hamlet takes in the play is in reaction to something that some other character does.

Hamlet's impetus to finally do something to avenge his father's death occurs when Hamlet has only minutes to live. Hamlet decides, finally, to kill Claudius, but this, too, was a reaction to Laertes's dying words, "The King, the King's to blame" (5.2.328).

If Laertes hadn't blamed Claudius for Gertrude and Hamlet's deaths in the final scene, Claudius might well have outlived Hamlet.

Hamlet’s inner struggles revolve around whether or not he should kill the king to avenge his father.  He is told by the ghost of his father that he needs to kill his uncle.  He is not happy with his uncle to begin with, because he did not feel that it was appropriate for him to marry his mother.   Hamlet feels conflicted about the process of murdering his uncle.  His struggles bring chaos to Denmark.

The approach that Hamlet takes is a little meandering.  He decides to pretend to be crazy so that he has free reign.  In the process, he really hurts Ophelia, who thought he loved her.  His crude behavior toward her saddens and confuses her.  His mother and uncle are also confused.  They even ask his friends Rosencrantz and Guildenstern what is going on with Hamlet, and his uncle finally sends him away while giving them instructions to kill him.

It is not that Hamlet never has any chances to kill his uncle.  Hamlet has a chance to kill Claudius when he sees him kneeling and he is vulnerable.  He thinks that his uncle is praying, and doesn’t want to kill him then because he feels that he will go to Heaven instead of Hell.  It turns out that he is not praying, because he found himself unable to do so, but Hamlet didn’t know that.

KING CLAUDIUS

[Rising] My words fly up, my thoughts remain below:
Words without thoughts never to heaven go. (Act 3, Scene 3) 

Hamlet's idea to have a play with a plot that is similar to the murder doesn't work out either.  He seems to have thought that his uncle would just confess and that would be that.  He doesn't.

Hamlet’s frustration with his mother leads to inner conflict as well. He is angry at her for marrying his uncle so soon after his father’s death.  He is a frustrated, confused, and angry young man.  This is why he accidentally killed Polonius.  He didn’t mean to, because Polonius had not wronged him.  However, that did not stop him from using Polonius’s body to continue his madness act.