The previous answers both link to the theme of 'public good versus personal benefit'.  Brutus kills a friend for the sake of Rome.  He puts his country's needs before his own. 

Another theme that  is strongly demonstrated through Brutus is  'lack of self-knowledge'.  Brutus is manipulated into believing that Caesar will become a tyrant and destroy Rome as a republic. (Remember that the term republic is not what we define as a 'republic' in modern era - the Roman republic did not give commoners voting rights for instance.)  

Brutus allows Cassius to be 'his mirror' and to dictate his thoughts and emotions.  Cassius cleverly flatters Brutus by telling him that Caesar is no better than Brutus, Caesar is not a god, but Brutus has the admiration and support of the people of Rome.  The Romans are looking at Brutus to save them from Caesar' tyranny.

If Brutus was more in touch with his own strengths and weaknesses, he would have identified Cassius as a manipulator.  He would have been able to question why Cassius hated Caesar so vehemently that he would attempt to humiliate Caesar to the extent where he compares him to 'a girl'.  Cassius launches a personal attack on Caesar.  Brutus should have been able to question this since he was a man with 'grey hair'  (wise) at this stage.  Yet, he does not, he accepts everything Cassius tells him and joins the conspiracy despite the fact that it troubles him so much that he is unable to sleep or find peace of mind. 

This reveals that Brutus does not understand enough about his own weakness, he is unaware of the fact that he is easily manipulated. He does not realise that he is being used by Cassius to reach a private goal (destroying Caesar out of envy) rather than acting for the good of Rome.  Shakespeare confirms this notion when Rome is destroyed after the killing of Caesar.  Both Cassius and Brutus die as well which leaves the audience with the question as to whether any of this would have taken place if Brutus did not allow himself to be manipulated by a man (Cassius) who was not thinking about the good of Rome in the first place.

There are undoubtedly many differences between Brutus and real Roman history, on the one hand, and Brutus and history as it is presented in Shakespeare's play Julius Caesar, on the other. I think we should focus on Shakespeare's Brutus and not try to analyze a Roman who lived over two thousand years ago. In other words, I think the question should not be "Why did Brutus kill Caesar" but why did Shakespeare's character Brutus kill the character Caesar. You can refer to a single soliloquy in Shakespeare's play for all the information about Brutus's motivation you should need. Here Brutus is telling the audience exactly why he has decided to join the conspirators in assassinating Caesar. That soliloquy (in my edition) is in Act 2, Scene 1, lines 10 through 34, beginning with "It must be by his death." This soliloquy contains some words of wisdom which have often been quoted:

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.

Brutus likes Caesar well enough but doesn't really trust him. Unfortunately, it is not in the least uncommon for friends to become enemies. Among other things, Brutus seems to be thinking that he would not be able to remain friends with Caesar if he became a king and a ruthless despot. Maybe Brutus is right. Brutus does not join the other conspirators frivolously but does a great deal of soul-searching. It was not easy for him to stab his friend. He was the last one of all to do so.

This is a great question. Indeed Brutus was friends with Julius Caesar. There is every indication there was genuine fondness. In light of this, it is odd that Brutus was marked as one of the conspirators.

The chief reason why Brutus was part of the conspiracy was due to his commitment to the principles of the Republic. Brutus believed in the Republic and wanted to pledge his loyalty to it. So, his love for the Republic was greater than his loyalty to his friend. In this sense, the tragic hero of the play is really Brutus.

Another reason for Brutus' part in the conspiracy was due to the enticements of the other conspirators. They fueled Brutus' worst fears that Julius Caesar was looking to make himself king and thereby end the Republic.

Finally, Brutus was part of long and venerable tradition of men who stood up against tryanny. His great ancestor was one of the men who expelled the kings from Rome to create a Republic.