What are some examples of effects of ambition in Julius Caesar?

There is ambition at work in many of the characters in the play.  Julius Caesar is assassinated because many of the other characters feel that he is too ambitious.  Their ambition, on the other hand, is what leads them to assassinate him.  They are ambitious enough to believe that they can do it and have that right.

Brutus, Cassius, and the other conspirators believed that Caesar wanted to make himself king of Rome. They were concerned that if they did not stop him he would continue grabbing power.  His march on Rome and the civil war against Pompey shook them.  Shakespeare alludes to this in the beginning scene with the commoners and Marullus and Flavius.

After killing Caesar, Brutus does not desire to replace himself as king.  He just wants to explain to the people that Caesar was too ambitious to live. He explains how much he loves Rome.

I weep for him;
as he was fortunate, I rejoice at it; as he was
valiant, I honour him: but, as he was ambitious, I
slew him. There is tears for his love; joy for his
fortune; honour for his valour; and death for his
ambition. (Act 3, Scene 2)

Brutus’s ambition is to rule Rome as a republic, as it was designed to be.  He is an idealist.  His speech, noble and ambitiously naïve, is followed by Mark Antony’s bombastic patriotism.  Antony does not excuse Caesar.  He carefully accuses Brutus and the others, and questions their charges of Caesar’s ambition, reminding the citizens what Caesar did for Rome. 

He was my friend, faithful and just to me:
But Brutus says he was ambitious;
And Brutus is an honourable man.
He hath brought many captives home to Rome
Whose ransoms did the general coffers fill:
Did this in Caesar seem ambitious?(Act 3, Scene 2)

We can’t talk about ambition without mentioning Octavius.  He is by far the most ambitious character in the play.  Most of his actions are subtle.  He is young, but he does not bow to Antony and follow his lead.  He takes most of Brutus and Cassius’s soldiers after his side wins the battle.  The fact that he has the last lines at the end of the play indicates that his plans are far-reaching.  Notice that he takes Brutus’s body, countering slightly Antony's comments about Brutus being the noblest Roman.

OCTAVIUS

According to his virtue let us use him,
With all respect and rites of burial.
Within my tent his bones to-night shall lie,
Most like a soldier, order'd honourably.
So call the field to rest; and let's away,
To part the glories of this happy day. (Act 5, Scene 5)

Octavius will later be extremely important to the history of Rome, and world history.  He was Rome’s first emperor.  His efforts to eliminate the competition, especially Mark Antony, are chronicled in Antony and Cleopatra.