1. Act I sc2. "O, that this too too solid flesh would melt...But break, my heart; for I must hold my tongue."
This soliloquy is spoken by Hamlet after he sees his mother whom Claudius has married, completely reconciled to her new state. She does not mourn the death of her husband (Hamlet's father) and seems happily married to Claudius. Hamlet is shocked at the change in his mother's attitude and this soliloquy expresses his disgust towards all women in the now famous line: "fraility thy name is woman!" In fact, he is so disgusted that he wishes that he could die and that he is even prepared to commit suicide. It is this soliloquy which has led many psychoanalytical critics to conclude that Hamlet suffers from an 'Oedipus Complex.'
2. Act I Sc5. "O all you host of heaven! O earth! what else?....I have sworn 't."
This soliloquy is spoken by Hamlet after the Ghost reveals to him how Claudius had murdered him. Hamlet is completely overwhelmed by hatred towards his uncle Claudius and vows to kill him in obedience to his father's wishes. Hamlet's father's ghost reminds him to never give up his idea of revenging his murder. So Hamlet practises what psychologists would today term as 'selective amnesia.' That is, deliberately forget everything that has been stored in his memory but always to remember only one thing - to kill his uncle Claudius and fulfill his father's ghost's wishes.