To be, or not to be. That is the question.
This is possibly one of the most famous quotes in Shakespeare's body of work, so much so that people who are not familiar with The Bard, and have never seen Hamlet performed on stage or screen, are still familiar with this line spoken by the Prince of Denmark. What they may not know is that the question that he is pondering is really about whether or not he should commit suicide. It is one of Hamlet's more philosophical moments, and he is questioning the meaning of life. Does existence offer him enough benefits to make him want to exist? He is on the fence about life, and the only thing that it seems to offer him that death does not is a kind of familiarity, or certainty, whereas what comes after death is so unknown that he is not sure he could truly embrace it or seek it out.
Horatio has a similar dilemma later in the film, as his friends are dead, or dying, around him. He decides to kill himself because he cannot bear to think of existing in a world that does not have Hamlet in it, although Hamlet manages to convince him to llive on, so that his story can be told.
The lady doth protest too much, methinks.
Hamlet has organized the staging of a play that mirrors almost exactly the murder of his father. Whilst she is watching it, Queen Gertrude utters this well-known observation; she is cynical about the character of Queen Hecuba in the play, specifically her avowed devotion to her murdered husband. Although she sounds sincere, Gertrude doubts her sincerity purely because she is so insistent in displaying it. Not only is Gertrude unconvinced by this devotion but she is also pragmatic about the relationship between husband and wife, and her comments suggest that she might not be as loyal or devoted to Claudius as he would like to believe; being her husband does not necessarily qualify him her automatic loyalty if she discovers that he has done something that betrays her, such as killing her husband or plotting to kill her son.
Get thee to a nunnery!
When Ophelia hands Hamlet back the trinkets and love tokens he has given her, he is distraught and extremely hurt. He has not yet realized that Polonius is behind her rejection of him, and assumes that she is cheating on him with someone else. The implication behind his comment is that she is acting in an flirtatious manner and needs to change her behavior. He sees her return of the love notes as a sign that she has been untrue, and thinks that she has betrayed him. Going to a nunnery would of course force her to undergo a period of time without any romantic or sexual contact whatsoever, and this is what he believes that she needs.
