Hamlet's first lines in the play are defiant, emotional and quick-witted in response to King Claudius (his uncle/step-father!) calling him "son", "A little more than kin and less than kind"(1.2 65) As the footnote in our Norton reveals to us, this one line carries a big punch- it serves as a means for Hamlet to backhandedly insult Claudius, announce his displeasure at the marriage between and his mother and Claudius and also introduces Hamlet as a poetic character. Perhaps this early development of Hamlet as a force not to be reckoned with in speech and discussion is why this play has more soliloquies than we've seen in other tragedies thus far.
Hamlet's first soliloquy in Act I Scene II divulges important information to the audience that is either partially already known by the other characters in the play or can only be known by the audience for the impending drama to unfold the way Shakespeare plans. Hamlet starts off in the midst of tragedy, Hamlet Senior has passed away, his ghost seems to be haunting the grounds of the Castle and just after a month of his death his wife remarried his brother and his son is still mourning. Because Hamlet (Jr.) is such an eloquent, intelligent character from the start he addresses us, the audience, alone and allows us into his inner thoughts rather than other characters and situations revealing important information to us (another one of Shakespeare's plot-development techniques).
"...O most wicked speed, to post
With such dexterity to incestuous sheets!
It is not, nor it cannot come to good.
But break, my heart, for I must hold my tongue"
If this ending to a soliloquy does not insinuate Hamlet's potential involvement in a tragic corrosion of what's left of his family (and himself), I'm not sure what would. Our main character, quick with his tongue and drenched in sorrow is so angry at his mother, angry at his father for leaving him in this position, upset that his father is gone and disgusted with his uncle seems to be insinuating that he is breaking. Could this breaking point destroy his family? Is Hamlet, the future prince of Denmark going to be a powerful character that creates his own tragedy (perhaps like Richard) rather than one that get's manipulated by the power of others (like Othello)?