The conspirators think that Caesar wants to destroy the Roman Republic and make himself king. He's already made himself dictator for life, so the next logical step is to go one better and have himself crowned, just like the Etruscan kings of old. Brutus and the other conspirators deeply venerate the Republic, which was founded after the Etruscan king Tarquin the Proud was overthrown in a popular uprising. From that day on, the very idea of kingship was anathema to the Romans, and woe betide anyone who gave the slightest impression that they wanted to revive the old Etruscan custom.

Caesar disavowed the crown in a very public show of forbearance, but none of the conspirators erre buying it. To them, it was nothing more than a gigantic charade designed to impress the plebs with Caesar's supposed modesty. They believe they know what Caesar really has in mind; they're stone-cold certain that he wants to make himself king and turn the Roman people into slaves. And the only way they can prevent this terrible fate from befalling the Republic is by having Caesar assassinated.

The conspirators view Julius Caesar as a threat to their positions of authority and fear that he will become emperor and disband the Senate. If Caesar were to become emperor, the senators' livelihoods would cease to exist, and they would lose their authority and influence in Rome. The conspirators also wish to increase their political power and wealth by eliminating Julius Caesar from his prominent position. Following Caesar's assassination, Cassius reveals that he was not concerned at all about the Roman populace and was instead selfishly motivated to kill Julius Caesar. Cassius proceeds to demonstrate his selfishness by selling political offices and accepting brides.

Out of all the conspirators involved in Caesar's assassination, only Brutus has purely honorable intentions. Brutus joins the conspirators because he fears that Caesar will rule Rome as a tyrant. Brutus likens Caesar to a "serpent's egg" and believes that his ambition will motivate him to rule as emperor (after Cassius has planted this idea in his mind). Unlike the other conspirators, Brutus is not selfishly motivated; he participates in the assassination in an attempt to protect the Roman populace from tyranny.

In short, Caesar's ambition is the impetus of the assassination plot.  His desire to become king is believed by the group of would be assassins to be an imminent threat to the current way of life.  Caesar's rule would overturn the republic, and Cassius concurs that Caesar is treated like a god though he is merely a man.