In act 1, scene 2 of William Shakespeare's Julius Caesar, Cassius is talking with Brutus on a street in Rome, trying to discover what's troubling Brutus, when a crowd of Roman citizens in another street raises a shout in praise of Caesar. Brutus remarks,

BRUTUS. What means this shouting? I do fear the people
Choose Caesar for their king (1.2.84–85).

This gives Cassius an opportunity to confide to Brutus that he, too, shares Brutus's concerns about Caesars ambitions. It also gives him the opportunity to remind Brutus that one of his ancestors, Lucius Julius Brutus, was instrumental in expelling the last king of Rome and became a founder of the Roman Republic almost 450 years ago. Since that time, no king has ruled over Rome, but Caesar is now giving every indication that he wants to be made king of Rome.

In February of 44 BCE, a month before the first scenes of Julius Caesar occur, Caesar declares himself "Dictator perpetuo," meaning "Dictator for Life." Brutus and Cassio learn from Casca that Caesar has just performed a deft bit of political theatre in front of a large crowd of Roman citizens by seeming to reject a crown offered to him by his friend Marc Antony, which only incites the crowd to urge Caesar to accept it.

Brutus invites Cassius to dinner the next evening so that they can discuss the matter further. Early the next morning, however, Cassius appears at Brutus's home with five other men, whose intent is to convince Brutus to join them in assassinating Caesar.

Brutus doesn't need much convincing. He's already wrestled with his own personal feelings about Caesar—in act 1, scene 2, Brutus tells Cassius that he's been "with himself at war" (1.2.51) about it— and he's thought about the issues of Caesar's unrestrained ambition and his increasing danger to the Roman Republic.

Brutus decides to join the conspirators and assumes the responsibility of organizing them for the assassination.

The reason why Brutus joins with the other conspirators is that Caesar's ambitions, his rise to nearly absolute power, his popularity with the people of Rome, his rejection of Roman institutions—such as the Senate, which he treats with contempt—and his desire to be king, all pose a serious and immediate threat to the Roman Republic. Brutus explains this succinctly in his oration to the people of Rome after Caesar's assassination.

BRUTUS. If there be any in this
assembly, any dear friend of Caesar's, to him I say that
Brutus' love to Caesar was no less than his. If then that
friend demand why Brutus rose against Caesar, this is my
answer: Not that I loved Caesar less, but that I loved Rome
more (3.2.19–24).

Unlike the other conspirators, Brutus is an honorable man with good intentions and views Julius Caesar as a serious threat to the Roman Republic. Brutus recognizes and fears Caesar's growing popularity, and Cassius convinces him that Caesar is an ambitious, dangerous man. Cassius warns Brutus that Caesar will eventually be crowned king and transform into a ruthless tyrant. Even though Brutus is relatively close friends with Caesar and holds no personal grudge against him, he does believe Caesar is capable of becoming an emperor and enslaving the population.

Brutus contemplates murdering Caesar and describes his motivation to join the conspirators during his soliloquy in act 2, scene 1. Brutus concludes that Caesar's ambition could influence him to abuse his power and likens Caesar to a "serpent's egg." In order to prevent Caesar from becoming king, disbanding the Senate, and enslaving the population, Brutus feels that it is necessary to kill him.

After Brutus and the senators brutally murder Julius Caesar at the Capitol, Brutus speaks before a large crowd and explains his actions. Brutus argues that Caesar was an ambitious man and describes his motives by saying the following:

If then that friend demand why Brutus rose against Caesar, this is my answer: not that I loved Caesar less, but that I loved Rome more. Had your rather Caesar were living and die all slaves, than that Caesar were dead, to live all free men?

Brutus feels that assassinating Julius Caesar was justified to protect the Roman citizens from tyranny. He is the only senator who does not act out of self-interest and is genuinely concerned about the well-being of Rome. One could conclude that Brutus's love for Rome motivated him to take Julius Caesar's life.

The main reason why Brutus believes that Caesar must die has to do with the people crowning Caesar as king; he believes that Caesar will have too much power, and may use this power in ways that might not best benefit Rome.  For example, Brutus states that, "Crown him?--that;--/And then, I grant, we put a sting in him,/That at his will he may do danger with." (Act II, scene i).  In other words, making Caesar king gives him far too much power, and would place him a position that negated the Senate's ability to temper his authority. 

It's important to note, though, that Brutus has no personal issue with Caesar.  In fact, earlier in this monologue, he says that, "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." (Act II, scene i).  Brutus sees his intention to murder Caesar as an emotionless, impersonal act that would save Rome from a would-be tyrant.