For let the gods so speed me as I love
The name of honor more than I fear death.
As explained in the thematic discussion there is much in the way of political dilemmas in the play. Brutus, in this same scene, lets it be know that he fears the people will anoint Caesar as their king, subordinating their liberty to him. In this quote, Brutus is explaining that his opposition to Caesar's rule is based on honorable intentions, and not selfish motives.
...and this man
Is now become a god; and Cassius is
A wretched creature, and must bend his body,
If Caesar carelessly but nod on him
Spoken by Cassius in the beginning of the play, the quote shows his motive of envy and resentment as the driving force behind his desire to eliminate Caesar. His motives contrast with the honorable motives of Brutus.
People and Senators, be not affrighted;
Fly not; stand still; ambition's debt is paid.
Spoken by Brutus directly after Caesar is slain, the quote points to one of the themes in the play: ambition. Brutus believes Caesar has been too ambitious and power-hungry, and that this has caused his death.
O, pardon me, thou bleeding piece of earth,
That I am meek and gentle with these butchers!
Antony, in a soliliquoy at the end of Act III, scene i, anguishes over the death of Caesar, who he considers "the noblest man that ever lived." The stage is set for the conflict between Antony and Brutus.
If then that friend demand why Brutus rose against Caesar, this is my answer,--
Not that I loved Caesar less, but that I loved Rome more.
Had you rather Caesar were living, and die all slaves, than that Caesar were dead, to live all freemen?
Brutus explains to the crowd of Roman citizens at Caesar's funeral why he rose against Caesar, indicating that it was for the good of Rome.
When that the poor have cried, Caesar hath wept:
Ambition should be made of sterner stuff:
Yet Brutus says he was ambitious;
And Brutus is an honourable man.
In a famous (or infamous) funeral oration, Antony cleverly turns the crowd against Brutus and the conspirators. He disputes Brutus's claim that Caesar was ambitious, telling the crowd that Caesar cried upon the deaths of poor people. In the final coup d'etat of the speech, Antony reads from Caesar's will, which stipulates money and property for the common people. The people begin to mutiny.
His life was gentle, and the elements
So mix'd him that
Nature might stand up
And say to all the world: "This was a man!"
His previous doubts cast aside, Antony submits that Brutus' motives were pure, and that his concern was for the Roman Republic, unlike the other conspirators. He was a true statesman.