Act 1, Scene 2. "O, that this too too sullied flesh would melt..."
Hamlet is fed up with the world and everybody in it. He sounds a little suicidal. He's grieving over his father's death, which he doesn't yet know was murder. He's angry with his mother, Gertrude, and his uncle, Claudius, and appalled that they got married—and, if that isn't bad enough, that they got married so soon after his father's death. He's torturing himself with how great his father was, how good things used to be between his father and his mother, and his mother's "incestuous" relationship with his uncle who is nowhere near as great as his father was.
This is Hamlet's first soliloquy. This soliloquy is character exposition, not character development, and it has nothing to do with the plot of the play.
"It is not, nor it cannot come to, good" (1.2.161)
Along with "Something is rotten in the state of Denmark" (1.4.99—which is often attributed to Hamlet, but is actually is spoken by Marcellus), and "My father's spirit in arms! all is not well" (1.2.274), this line is far too general to be considered either prophecy or foreshadowing.
Act 1, Scene 5. "O all you host of heaven!..."
Just prior to this soliloquy, the ghost of Hamlet's father appears to Hamlet and tells him that Claudius murdered him. The ghost then asks Hamlet to "Revenge his foul and most unnatural murder." (1.5.29)
Now to my word:
It is ‘Adieu, adieu! Remember me.’
I have sworn't. (1.5.115-117)
Hamlet resolves to revenge his father's murder, and he swears to Heaven, earth, and Hell to avenge his father's murder and even writes it in his brain to remember forever and forever. But Hamlet doesn't avenge his father's murder. Instead, he does little more than look into the situation. He investigates it. He conducts experiments. He acts crazy. He makes excuses for not doing anything about his father's murder.
This soliloquy does little to develop Hamlet's character, and although Hamlet swears to move heaven and earth to revenge his father's murder, he doesn't do anything.
Act 2, Scene 2. "Now I am alone..."
Hamlet berates himself and calls himself names for many, many lines for doing absolutely nothing about his father's murder, then he calls Claudius names. Then he makes another excuse for not avenging his father death like he swore he would.
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.
The play's the thing
Wherein I'll catch the conscience of the King. (2.2.593-600)
This is where Hamlet finally has an effect on the plot of the play! Hamlet has arranged for the Players to insert some lines into the play-within-a-play that they're going to perform at court that evening, and "If he [Claudius] but blench, / I know my course." (2.2.592-593)
Act 3, Scene 1. "To be or not to be..."
If a tree falls in the forest, and no one is there to hear it, does it make a sound? Is a soliloquy really a soliloquy if another character is listening to it? Is a soliloquy really a soliloquy if another character is listening to it, but the character doing the soliloquizing doesn't know that another character is listening?
Consider this scenario:
CLAUDIUS. For we have closely sent for Hamlet hither,
That he, as 'twere by accident, may here
Her father and myself, lawful espials,
Will so bestow ourselves that, seeing unseen,
We may of their encounter frankly judge
And gather by him, as he is behaved,
If't be the affliction of his love or no,
That thus he suffers for.
POLONIUS. Ophelia, walk you here. Gracious, so please you,
We will bestow ourselves. Read on this boo...
POLONIUS. I hear him coming. Let's withdraw, my lord.
HAMLET. To be, or not to be, that is the question...
...Soft you now!
The fair Ophelia! Nymph, in thy orisons
Be all my sins remembered. (3.1.32-97)
Claudius, Polonius, and Ophelia have been listening to Hamlet talking to himself. It appears, too, that Claudius has been paying close attention to what Hamlet has been saying.
CLAUDIUS. Love? His affections do not that way tend;
Nor what he spake, though it lack'd form a little,
Was not like madness. (3.1.171-173)
Nevertheless, although this soliloquy (if that's what it really is) seems to give some insight into Hamlet's character, much depends on whether Hamlet is aware that other character are listening to him and on whether Hamlet says what he says because someone is listening. Even if he can't see Claudius and Polonius, Ophelia is in the same room with him, walking around and supposedly reading a book. Does Hamlet not see her?
If, as some scholars and others argue, Hamlet is contemplating suicide, "His affections do not that way tend." Just because Hamlet is talking about suicide doesn't necessarily mean that he's actually considering killing himself.
As if often the case with Hamlet (see the "Now might I do it pat" soliloquy below), he finds ingenious ways of not doing things. If Hamlet was at all considering suicide, by the end of the soliloquy he's talked himself out of it.
Another consideration is that in the First Quarto of Hamlet, published in 1602, this soliloquy was spoken by Hamlet before the arrival of the players in Act 2, Scene 2. In the Second Quarto, published in 1604—ironically called the "bad" quarto—this soliloquy appears in its present location in Act 3, Scene 1, as it does in the First Folio, published in 1623.
How, then, does the location of the soliloquy within the play affect its significance regarding Hamlet's character and/or the plot of the play. The soliloquy might still reveal something about Hamlet's character in either location, but if the soliloquy can be moved from one act to another, it would appear that it has little influence on the plot.
Act 3, Scene 2. "[T]is now the very witching time of night..."
Hamlet is still pretty excited about Claudius's reaction to the play-within-a-play, and he's ready to "drink hot blood" and do whatever else it takes to revenge his father's death. He's also going to march right into his mother's room and tell her exactly how he feels, exactly how things are, and exactly what he's going to do about it.
It's big revenge talk, just like the rest of his big revenge talk.
There's nothing new about Hamlet's character in this soliloquy. There's also nothing in the soliloquy that affects the plot.
To his credit, Hamlet does speak harshly to his mother in the next scene, like he said he would. He also accidentally kills Polonius which actually does affect the plot—certainly more than speaking harshly to his mother—but killing Polonius isn't something that Hamlet did on purpose, and it's not something that arose from anything Hamlet said in this soliloquy.
Act 3, Scene 3. "Now might I do it pat, now he is praying..."
Hamlet walks into a room where Claudius is on his knees, lost in his own thoughts, praying silently. Nobody else is in the room. It's just Hamlet and Claudius. This is a perfect opportunity for Hamlet to kill Claudius and avenge his father's murder.
What does Hamlet do? Nothing. Claudius is kneeling there, right in front of him, totally defenseless, and Hamlet talks himself out of killing him.
This is nothing new. This situation is simply more dramatic than the usual ways that Hamlet finds to do nothing to revenge his father's death. There are no revelations about Hamlet's character in this soliloquy.
It might be argued that Hamlet has moral and ethical reservations about killing Claudius while he's praying that reveals something about Hamlet's character that the audience didn't already know. It could also be argued that what Hamlet says and what Hamlet doesn't do simply reinforce what the audience already knows about his character.
This soliloquy does nothing to affect the plot.
It might be argued that Hamlet's decision not to kill Claudius affects the plot significantly, in the sense that if Hamlet did kill Claudius right then, the play would be over. This not so much develops the plot as simply ends it.
Act 4, Scene 4. "How all occasions do inform against me..."
This time, rather than simply castigating himself in general, Hamlet compares himself specifically to Young Fortinbras. Hamlet find himself utterly deficient in his decision-making ability, and in his inability to follow through on the things he resolves and swears to do. Hamlet even calls himself a coward.
From the depths of self-degradation, Hamlet cries out:
O, from this time forth,
My thoughts be bloody, or be nothing worth! (4.4.67-68)
The audience has heard all of this before. The audience learns quite early in the play what they need to know about Hamlet's character, and his essential character changes very little throughout the play. Hamlet doesn't act. Hamlet reacts, very slowly, if at all, to the situations and circumstances around him. What Hamlet does is talk.
What Hamlet says in this soliloquy has the same effect on the plot as everything he's said in every other soliloquy, except perhaps for "The play's the thing / Wherein I'll catch the conscience of the King" in the soliloquy in Act 2 , Scene 2.