In the classical sense of the term, I believe Brutus is a hero. That doesn't mean that what he does is a good thing. A classical tragic hero is always a member of the nobility, always has some kind of tragic flaw, and is doomed to make a serious error in judgment. Brutus fulfills those requirements. In my opinion, his tragic flaw is his intense loyalty to the republic. It is so intense and he is so adamant that there should never be another king in Rome that he cannot detect the envy in Cassius criticism of Caesar, and he interprets Caesar's actions as signs that Caesar indeed plans to declare himself king.
Of course, Caesar was also a tragic hero.