The only conspirators who expressed reasons for assassinating Caesar were Cassius and Brutus. Shakespeare had a lot of history to condense into a stage play, and he relied heavily on Plutarch's "Life of Julius Caesar," "Life of Brutus," and "Life of Antony" in English translations. The real Julius Caesar was a remarkably dynamic man who intended to become the supreme ruler of the Roman Empire in order to solve the many economic, political, and military problems the empire was facing. There were people who wanted a "strong man," on the order of Mussolini, Hitler, and Stalin. There were people who feared such a strong man because he threatened their privileged positions. Cassius was motivated by envy and fear for his personal safety. He knows that Caesar dislikes him and might even have him killed. It is significant that in Act 1, Scene 2, he says to himself:
Caesar doth bear me hard; but he loves Brutus:
If I were Brutus now and he were Cassius,
He should not humour me.
Like some of the other conspirators, Cassius has only selfish reasons for wanting Caesar assassination. He would gladly accept Caesar as king if he thought it would do him any good. Only Brutus has logical, unselfish reasons for participating in the plot. He expresses them in a famous soliloquy in Act 2, Scene 1:
It must be by his death: and for my part,
I know no personal cause to spurn at him,
But for the general. He would be crown'd:
How that might change his nature, there's the question.
It is the bright day that brings forth the adder;
And that craves wary walking. Crown him?--that;--
And then, I grant, we put a sting in him,
That at his will he may do danger with.
The abuse of greatness is, when it disjoins
Remorse from power: and, to speak truth of Caesar,
I have not known when his affections sway'd
More than his reason. But 'tis a common proof,
That lowliness is young ambition's ladder,
Whereto the climber-upward turns his face;
But when he once attains the upmost round.
He then unto the ladder turns his back,
Looks in the clouds, scorning the base degrees
By which he did ascend. So Caesar may.
Then, lest he may, prevent. And, since the quarrel
Will bear no colour for the thing he is,
Fashion it thus; that what he is, augmented,
Would run to these and these extremities:
And therefore think him as a serpent's egg
Which, hatch'd, would, as his kind, grow mischievous,
And kill him in the shell.
I inadvertently posted my answer before trying to respond to the question: "Do you think they were justified in killing Julius Caesar?"
This seems more like a historical question. Julius Caesar was actually assassinated for many complex reasons which Shakespeare could not deal with in a stage play. In the first half of Julius Caesar, Shakespeare makes the audience sympathize with the conspirators, largely because Brutus is the leader and seems like such an honorable and sincere character. But then Shakespeare, in obedience to actual history, turns the play completely around and makes the audience sympathize with Mark Antony and Octavius because they were, after all, on the winning side in history.
I don't know whether I think they were justified in killing Julius Caesar. I don't think Shakespeare cared especially whether they were right or wrong. He was just trying to make drama out of real history. We can sympathize with Caesar, with Brutus, with Antony, and with Octavius, but not with Cassius, who instigated the whole plot for selfish reasons.
It seems to me that if Julius Caesar had become king or emperor, he would have ruled in a way very similar to that actually done by his heir Octavius Caesar. It would seem that the empire was evolving from a republic into a monarchy and would have done so regardless of who became the supreme ruler. We in the United States of America should be concerned about how our own nation is evolvinig from an small and weak isolationist democracy into a world empire. Nothing ever remains the same. Everything is always changing.