The key moment when religion affects Hamlet's behavior is when he is presented with the opportunity to avenge his father's death, as the former king has requested in a ghostly vision several scenes earlier. Hamlet has spent a great deal of mental energy up to this point trying to discern the truth about the claims of the ghost. He becomes certain that Claudius has murdered his father after the Mousetrap Play and could choose at this point to end his life. Yet Hamlet doesn't do so, because he believes Claudius is praying:

Now might I do it pat. Now he is a-praying.
And now I’ll do ’t. And so he goes to heaven.
And so am I revenged.—That would be scanned.
A villain kills my father, and, for that,
I, his sole son, do this same villain send
To heaven. (III.iii.77–82)

Hamlet doesn't spare Claudius because he believes him a sincere and repentant man; instead, he believes that because Claudius is praying, killing him in that moment would be a reward of sorts—sending Claudius to Heaven, while his own father's ghost is in Purgatory. This religious view of Hell, Heaven, Purgatory, and judgement reflects Hamlet's personal religious beliefs that shape his decisions. Instead, Hamlet plans to delay his revenge so that Claudius's "soul may be as damned and black / As hell, whereto it goes" (III.iii.98–99). Religion guides Hamlet to this delay; his final destiny also evolves from this decision, as Claudius's death becomes interwoven with his own.

Religion also guides a peaceful resolution with Laertes just before he and Hamlet die. Laertes forgives Hamlet for killing his own father, Polonius, and asks for Hamlet to forgive him for causing his death. Hamlet acknowledges that God has already forgiven Laertes, and he dies with his plans for revenge adequately fulfilled and with God's forgiveness comforting his soul as he exits the world.

Hamlet's Christian faith has an enormous impact on his behavior and decisions throughout the play. Hamlet's faith prevents him from committing suicide as a means of escaping his severe depression and also hinders his decision to murder Claudius in order to avenge his father's death. In act one, scene two, Hamlet illustrates how his Christian faith affects his decision to not commit suicide by saying,

"Oh, that this too, too sullied flesh would melt, Thaw, and resolve itself into a dew, Or that the Everlasting had not fixed His canon 'gainst self-slaughter! O God, God!" (Shakespeare, 1.2.129–132).

Hamlet's Christian beliefs also impact his willingness to trust his father's ghost, which motivates him to search for more concrete evidence that Claudius assassinated his father. In act two, scene two, Hamlet begins to develop a scheme that will allow him to prove whether or not Claudius actually murdered his father. The following quote illustrates how Hamlet's faith influences his decision to search for more evidence:

"May be the 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" (2.2.562–566).

In act three, scene three, Hamlet enters the room while Claudius is attempting to pray. Hamlet finally has a prime opportunity to kill Claudius and avenge his father's death, but he hesitates because of his Christian beliefs. Hamlet refuses to kill Claudius because he believes that he will essentially be doing Claudius a favor by sending his soul to heaven. Hamlet believes that Claudius's soul would go to heaven if he were to die while asking God for forgiveness. Hamlet's comments once again reveal how Christianity impacts his behavior:

"Now might I do it pat. Now he is a-praying. And now I’ll do ’t. And so he goes to heaven. And so am I revenged.—That would be scanned. A villain kills my father, and, for that, I, his sole son, do this same villain send To heaven. Oh, this is hire and salary, not revenge. He took my father grossly, full of bread, With all his crimes broad blown, as flush as May. And how his audit stands who knows save heaven?" (Shakespeare, 3.3.74–83).

Religion is alluded to by Hamlet and spoken of directly in his opening soliloquy of Act I, scene ii ("Or that the Everlasting had not fix'd/His canon 'gainst self-slaughter").  However,  the play's most striking infusion of Christian ethics relates to the ghost's decree to Hamlet to "[r]evenge his foul and most unnatural murder."  As Kenneth Muir notes in his essay on the Ghost found in the Enotes Study Guide on Hamlet (linked below):

According to the various beliefs current in Shakespeare's day, a ghost could be. . . a spirit come from purgatory by divine permission or a devil disguised as a dead person in order to lure the living into mortal sin.

And whichever of these the Ghost might be is crucial to Hamlet's decision to follow its words and guidance or not.   Christian doctrine would dictate that he shun the request of a "devil" but pursue and complete the request of "a spirit come from purgatory by divine permission."  But which one is this ghost?  This is a major dilemma for Hamlet in the play, one that is resolved when Hamlet presents The Mousetrap and catches "the conscience" of his uncle, the murderer of his father.

So Hamlet's delay in revenging his father's murder is due, in part at least, to the question of whether the spirit of his father is divine or dammed.  As a good Christian, Hamlet must decide which the ghost is before he takes the spirit's word at face value and pursues the commanded revenge.  In this way, religion has a monumental affect on Hamlet and his choices/behaviour.

For more on the religious significance of the Ghost as it relates to Hamlet , please see the essays linked below.

How is religion relevant to William Shakespeare's Hamlet?

Religion plays an obviously crucial role in William Shakespeare’s Hamlet. Religion is mentioned repeatedly in the play, and religious issues are often the subject of extended discussion. To mention just two instances: Hamlet seems to contemplate the possibility of suicide in his famous “To be or not to be” soliloquy, and at the end of that speech he seems to refrain from suicide, in part, because he cannot be sure what will happen to his spirit after his death. Fear of the aftermath of death, as much as any desire to continue living, prompts Hamlet to refrain from killing himself.  Another scene in which the importance of religion is obviously important is the scene in which Claudius tries to pray as Hamlet stands secretly and quietly nearby, wondering whether he should take advantage of this opportunity to kill the new king.  Ultimately, Hamlet decides against such a course of action. Yet he makes this decision not so much because he thinks that killing Claudius would be a violation of religious law, but rather because he worries that if he kills Claudius as Claudius tries to pray, he may, ironically, send Claudius to heaven (and perhaps himself to hell). In other words, very pragmatic considerations, rather than deeply religious worries, prevent Hamlet from taking advantage of his opportunity to murder Claudius.

One of the major debates concerning religion in Hamlet concerns which religious ethic, if any, applies to this play.  Should we see the play’s events from a Protestant point of view? If so, then the ghost (according to many critics) is almost surely an evil spirit sent by Satan to tempt Hamlet to commit a crime that will damn his soul to hell.  Protestant readings of the play are more likely than other kinds of readings to see the ghost as evil. On the other hand, readings rooted in Catholic theology are more likely to consider the ghost a figure briefly released from Purgatory in order to help right a serious spiritual wrong (Claudius’s murder of the old king). According to this approach, the ghost is not necessarily an evil spirit and may indeed function as an instrument of divine justice. Finally, yet another approach – which might be called a “pagan” approach – would suggest that few Elizabethans would really have been troubled by Hamlet’s plans for revenge or by the ghost’s efforts to encourage revenge.  According to this approach, most Elizabethans would have sympathized with Hamlet’s to discover the truth about his father’s death and to avenge himself on Claudius when Hamlet becomes convinced that Claudius is indeed the murderer of his father.  These readers would point to the praise of Hamlet offered by Horatio at the end of the play. If Horatio (these readers would argue) is not shocked and disgusted by Hamlet’s behavior, neither should we be. After all, near the very end of the final scene, Horatio says to the dead or dying Hamlet,

Now cracks a noble heart. Good night, sweet prince, 
And flights of angels sing thee to thy rest!

Horatio seems to assume that Hamlet is not going to hell but to heaven. Horatio, in other words, does not seem to have any religious qualms about Hamlet’s conduct.

Religious interpretations of the play, however, are many and varied and are often in great conflict with one another.

What is the role of religion in Hamlet?

When looking at the role of religion in the play Hamlet, you might want to point out that it is not a typical religious play. However, religion still plays an important role, as it is frequently mentioned throughout.

For example, religion occasionally determines the way people act. This can be seen when Hamlet contemplates killing Claudius but then chooses not to because he is aware of the fact that Claudius is praying. Hamlet believes in heaven and hell, and he wants to ensure that Claudius goes to hell. He fears that Claudius might end up in heaven if he dies while praying:

And am I then revenged
To take him in the purging of his soul
When he is fit and season'd for his passage? (3.3.85–87)

You could, therefore, argue that it is Hamlet’s religious belief that prevents Claudius’s murder at this point in the play.

Another example of religion playing an important role in the play is in the character of Claudius. Not only do we see him praying in the scene described above, but he also refers to his faith later on. For example, he believes firmly that God will protect him:

Do not fear our person.
There’s such divinity doth hedge a king
That treason can but peep to what it would,
Acts little of his will. (4.5.97–100)

Because of this erroneous religious belief, Claudius acts the way he does and he still feels invincible. Therefore, you could argue that Shakespeare uses religion in order to show how it impacts and influences peoples. In the case of Claudius, you could claim that Shakespeare shows his audience how powerful people try to abuse religion in order to justify their actions.

How does religion help or hinder the characters in William Shakespeare's Hamlet?

While Hamlet is set in Protestant Denmark, it was rumored that Shakespeare, whose father John was a Roman Catholic, was a closet Catholic. Perhaps, this explains why some of the doctrine of Catholicism emerges in this play.

At any rate, Hamlet continues his own life and allows Claudius to continuing living as he restrains himself from committing two murders because of his religious beliefs.

1. [Notice the use of the word canon, which is used in Catholicism]: 

O, that this too too sallied flesh would melt,
Thaw, and resolve itself into a dew,
Or that the Everlasting had not fixed
His canon 'gainst self-slaugher. (1.129-132)

Hamlet is motivated to not commit suicide, even though he would like to die, because he believes it is a mortal sin and he would go to hell. (Later on, Ophelia cannot be buried on consecrated ground because she killed herself as Catholicism forbade such burials.)

2. As Hamlet watches Claudius pray after leaving the Dumb Show in which the king is murdered by poison being poured in his ear in imitation of Claudius's heinous act against his brother Hamlet.

O, my offence is rank, it smells to heaven;
It hath the primal eldest curse upon't
A brother's murder. Pray can I not,
Though inclination be as sharp as will.
My stronger guilt defeats my strong intent, (3.3.

When he hears Claudius confess his fratricide, Hamlet sees his opportunity for revenge, but he changes his mind as he realizes that with Claudius at prayer, his murder would make the villain a martyr (another Catholic concept), "purging his soul" (3.3.85), and send him to heaven. So, Hamlet waits so that "his [Claudius's] soul may be as damned and black/As hell... (3.3.94-95).

How does religion help or hinder the characters in William Shakespeare's Hamlet?

William Shakespeare's Hamlet is a revenge tragedy full of murder and almost-incestuous relationships. Those do not sound like the typical elements of a story that is at all concerned with religious themes; however, the issues of mortality and the afterlife play a significant role in this play.

Hamlet was written in the 16th century in England, when religion was a tremendous source of violence and anxiety. The Protestant Reformation introduced a new kind of religious thinking to the English people, and the way Catholics and Protestants saw the important issues of life and death were still confusing to people at this time.

We know that Hamlet's constant indecision is the cause of most of the trouble he and other characters face throughout the course of the play; consider the reason for his indecision. We hear it from him almost from the first time we meet him, and it is a consistent theme throughout the play.

Hamlet is despondent because his father is dead and his mother has remarried much to quickly--and her new husband is her old husband's brother. That would cause some consternation for a young man who is sensitive to the issues of life, death and the afterlife. In his first soliloquy, Hamlet says:

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! 

Clearly the only reason he does not commit suicide is because he believes God ("the Everlasting") has proclaimed it a sin. 

Later, in Act III, Hamlet speaks these lines in a soliloquy:

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 bourn

No traveler returns, puzzles the will

And makes us rather bear those ills we have

Than fly to others that we know not of?

Hamlet both acts and fails to act because of his religious beliefs. Denmark and nearly everyone in this play is impacted by those actions and inactions: Polonius, Ophelia, Laertes, Claudius, Gertrude, Hamlet, and even Horatio and Fortinbras.