Quite simply, it is Caesar's way of elevating himself above everybody else, god like almost. He is the only character in the play to speak of himself in the third person. In his mind, he is already emperor of Rome, and all that remains is the formal ceremony. That he refuses the crown three times is part of his strategy. It just makes the people want him more.
Cassius is correct in his observation of Caesar when he is trying to convince Brutus of the danger he poses to Rome. He compares him to a Colossus striding through Rome implying stepping on others along the way.
Are Cassius's fears correct? One has only to look at the history of Rome and the change from a Republic to an Empire to find the answer.