Here are some selected famous quotes, in the order they appear in the play.

Beware the Ides of March.
(Soothsayer, Act 1 Scene 2)

Men at some time are masters of their fates.
The fault, dear Brutus, is not in our stars
But in ourselves, that we are underlings.
(Cassius, Act 1 Scene 2)

Yond Cassius has a lean and hungry look:
He thinks too much: such men are dangerous 
(Caesar, Act 1 Scene 2)

But, for mine own part, it was Greek to me. 
(Casca, Act 1 Scene 2)

Let's carve him as a dish fit for the gods.
(Brutus, Act 2 Scene 1)

When beggars die there are no comets seen: 
The heavens themselves blaze forth the death of princes.
(Calphurnia,Act 2, Scene 2)

Cowards die many times before their deaths, 
The valiant never taste of death but once. 
(Caesar, Act 2 Scene 2)

Et tu, Brute?—Then fall, Caesar.
(Caesar, Act 3, Scene 1)

Cry havoc and let slip the dogs of war.
(Antony, Act 3 Scene 1)

Not that I loved Caesar less, but that I loved Rome more.
(Brutus, Act 3 Scene 2)

Friends, Romans, countrymen, lend me your ears. 
(Antony, Act 3, Scene 2)

This was the most unkindest cut of all. 
(Antony, Act 3 Scene 2)

There is a tide in the affairs of men. 
(Brutus, Act 4 Scene 3)