What are some important quotes spoken by the character Macbeth in Shakespeare's play?

It is difficult to choose only a few lines to pull out of the play for Macbeth, but here are some examples that indicate Macbeth’s journey and are important to showing who he is as a character, his state of mind, and the direction of the plot.
The first important one is Macbeth’s reaction to Malcolm being named successor to the throne.  The witches indicated that Macbeth would be king, and he really wants to be king.  He does not take Duncan’s announcement that his son will be king well.

MACBETH
[Aside] The Prince of Cumberland! that is a stepOn which I must fall down, or else o'erleap,For in my way it lies. Stars, hide your fires;Let not light see my black and deep desires … (Act 1, Scene 4) 

This shows that Macbeth is ambitious, and that he is worried about the effects of his ambitions.  He does not want to show others how much he wants to be king, and how disappointed he is in not being chosen.  This is especially true because no one probably expects him to think he will be king, since it makes more sense for the king’s son to be king. 
Another significant quotation from Macbeth comes from when he is trying to decide what to do about this discrepancy between his wishes and Duncan’s.  He imagines a fantasy dagger, and wonders where it came from.  Does this mean that he is meant to kill Duncan and become king himself?

Is this a dagger which I see before me,The handle toward my hand? Come, let me clutch thee.I have thee not, and yet I see thee still.Art thou not, fatal vision, sensibleTo feeling as to sight? or art thou butA dagger of the mind, a false creation,Proceeding from the heat-oppressed brain? (Act 2, Scene 1)

Macbeth’s wife wants him to be a man and swallow his doubts, but he is grappling with the moral and practical questions of killing the king.  When he sees the dagger, it is partly a manifestation of his ambition.  It gives him the courage to do the deed, but it does seem to add to the impression that he is hardly sane!
Another significant quote is Macbeth’s reaction to his wife’s death.  He seems to ponder his own mortality along with hers.  She has succumbed to her own guilt at their deed, and he is getting more and more unstable.

To-morrow, and to-morrow, and to-morrow,Creeps in this petty pace from day to dayTo the last syllable of recorded time,And all our yesterdays have lighted foolsThe way to dusty death. Out, out, brief candle!Life's but a walking shadow, a poor playerThat struts and frets his hour upon the stageAnd then is heard no more: it is a taleTold by an idiot, full of sound and fury,Signifying nothing. (Act 5, Scene 5)

Macbeth has seen nothing turn out as he hoped.  He did become king, but he had to hold on to his power with more and more bloodshed, always fearing to lose it.  As he makes this speech, his wife is dead and Malcolm’s troops are storming the castle.  Macbeth’s power is threatened, and his own mortality is on his mind.