To be, or not to be. That is the question.
This is quite possibly the most famous line in any of Shakespeare's works. It is situated in one of Hamlet's more philosophical moments as he wonders whether it is better to exist or not exist. Should he commit suicide, or should he keep living? The question sums up Hamlet's general indecisiveness that is evident throughout the film. In the end, he decides that he is going to keep living, but not because he is convinced that life is a better option; he is merely uncertain about what happens after death.
The lady doth protest too much, methinks.
This is another of those Shakespearian quotes that is used in many situations without knowledge of where it comes from. In fact it is spoken by Gertrude, while watching the play that Hamlet hopes will reveal her reaction, and also Claudius', to the murder that mirrors the murder of his father. Queen Hecuba, in the play, commits herself to her husband who is about to be murdered and Gertrude's observation that she "protests too much" suggests that she is cynical about Hecuba's seeming devotion to her husband, and doubts her sincerity. She is also suggesting that although she has married Claudius her marriage vows do not guarantee her loyalty to him.
I am but mad north-north-west. When the wind is southerly, I know a hawk from a handsaw.
Hamlet is speaking to Rosencrantz and Guildenstern when he is describing his madness. His words suggest that just as the wind only blows occasionally from the north-north-west, so his he only occasionally insane. The words are also a warning to his former friends; even when he appears to be mad, he did not come down in the last shower, and he is still able to distinguish a hawk from a handsaw - or in their case, a friend from a foe.