The conspirators had a wide range of motives for murdering Julius Caesar. Shakespeare bases his play on material primarily from Plutarch, but Cicero's letters also provide an excellent portrait of the politics of the period.
The first political issue at stake was the balance of power between the plebeians and the Senate. Julius Caesar himself was popular with the plebs and was trying to use his personal popularity to circumvent the Senate and to become increasingly monarchical. Members of the Senate felt that he was bribing the masses with "bread and circuses" to solidify his own position as a tyrant. Brutus, in particular, was concerned that Caesar's personal power would mean the end to the Republic. Of all the conspirators, Brutus, "the noblest Roman of them all," seems to have been motivated purely by ethical concerns.
Cassius and some of the other conspirators appear to have been motivated more by jealousy and desire to maintain their Senatorial powers and prerogatives.