Julius Caesar is described as ambitious by his enemies. Whatever may be said of him, he wants to be well thought of by everyone. He is vain and perhaps self-centered. It. is not necessarily clear that he is indeed, ambitious. He does work hard, as he refuses to stay home from the Senate because of Calphurnia's dream (athough it is because a "friend" has interpreted the dream in a way to appeal to his vanity, making the horrible dream into one that honors him throughout all of Rome). He refuses the crown not once, but three times.
He also suffers from the "falling down" sickness or epilepsy, which could concern Caesar as appearing weak in the eyes of his fellow Romans. He seems to be always alert as to outward appearances.
Caesar is also seen as a superstitious man who views Cassius as one with a "lean and hungry look". He doesn't trust very many, and the ones he does trust--Brutus--betrays him.
He could also be seen as hard and unfeeling since he treats Calphurnia with such disregard when he openly requests that Mark Antony touch her during the Feast of Lupercal to heal her barrenness. It is not unusual that he wants a son, but it is insensitive to request it in this manner for his wife.