This is a good question. Julius Caesar was a towering figure in the ancient world and in Shakespeare's work. Julius Caesar was a conquering general and accumulated many more titles and honors. Most significantly, he was proclaimed dictator for life, which was the first time in Roman history anyone ever did this. As for Caesar's motiviation, we cannot be sure. Was he aiming for "kingship" or something akin to this? It is impossible to say.
As for Brutus and Cassius, they believed that Caesar transgressed the Republican boundaries. Within Republican views, no one person should have that much power and most of all true Republicans hated anything to do with kingship. For this reason, Brutus and Cassius joined in the conspiracy to kill Caesar.
In light of these points, Brutus and Cassius wanted a Republic, and Caesar wanted something more for himself.