What is the importance of the crowd scenes in Julius Caesar?Julius Caesar by William Shakespeare

In Shakespeare's Julius Caesar, the
reactions of the crowd--mob rule--are what lend meaning first to the speeches of
Cassius, Brutus, and then to that of Marc Antony, thus propelling the action of the
play.  For instance, in Act I, Scene Two, in what has come to be known as "the seduction
scene," Cassius seeks to persuade Brutus that Caesar is power-hungry.  He tells Brutus
that when Caesar triumphantly entered the streets of Rome after having defeated Pompey,
Marc Antony offered him a crown--a "coronet":

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Then he offered it to him again; then he put it
by again; but to my thinking, he was very loath to lay his fingers off it.  And he
offered it the third time.  He put it the third time by; and still as he refused it, the
rabblement hooted, and clapped their chopt hands, and threw up their sweaty nightcaps,
and uttered such a deal of stinking breath because Caesar refused the
crown....(I,ii,239-246)

Here
Cassius makes reference to the crowd to impress upon Brutus the power lust of Caesar, as
well as to illustrate how Marc Antony can manipulate a crowd.  In fact, this scene
foreshadows the future manipulation of the Roman crowd by Antony in Act III.  That
Cassius understands this weakness of the Romans in the meek acceptance of the
appearances of things is exhibited in his statement to Brutus in Act
I:

The Romans
now/Have thews and limbs like to their ancestors;/But woe the while!  Our fathers' minds
are dead,/And we are governed with out mothers'Spirits;/ Our yoke and sufferance show us
womanish. I,ii,80-84)

Then,
in Act III, after Brutus and the other conspirators assassinate Caesar, Brutus prepares
to speak to the crowd,  Antony approaches and asks permission to also address them. 
Against the wise advice of Cassius who understands mob mentality, Brutus gives his
permission provided Antony not blame the conspirators and he is allowed to speak first. 
As Brutus speaks to the Romans, he places his faith in the logical reasons he provides
for Caesar's death:

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Believe me for mine honor, and have respect to
mine honor, that you may believe.  Censure me in your wisdom, and awake your senses,
that you may the better
judge....(III,ii,14-20)

Brutus
then addresses the crowd and asks any to speak "for him have I offended.  I pause for a
reply" (III,ii,33-34)  The crowd is positively persuaded and reply "None, Brutus, none!"
(III,ii,35)

However, with Marc Antony enters with Caesar's
body and shows the crowd where all the daggers have gone, the "womanish" crowd is
emotionally swayed.  With rhetorical devices such as repetition and tone of voice,
and irony, along with the reading of Caesar's will as an example of his altruism, Antony
persuades the crowd that Caesar was senselessly
murdered:

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They were villains,
murderers!

O piteous
spectacle!

O noble Caesar!

O
most bloody sight!

We will be
revenged!

Revenge!  About!  Seek!  Burn!  Fire!  Kill! 
Slay!  Let not a traitor live!
(III,ii,199-206)

Clearly,
emotional appeals sway the crowd more than rational ones.  An ensuing civil war begins
as a result of the persuasive arguments of Marc Antony who in the first act proves that
he knows how "to work the crowd" to his advantage.  This crowd, then, in
effect, initiates the demise of Brutus and Cassius and the triumph of Antony, Octavian,
and Lepidus, the second triumvirate.