At the end of Act I, a terrible storm comes up. Casca and Cicero each believe that the storm foreshadows events surrounding Caesar's impending assassination. Casca is fearful of a host of strange sightings and believes that these signs prognosticate evil. Cicero believes that the storm's power mirrors the power of the conspirators. Cassius is also energized by the storm.
Caesar's wife, Calpurnia has a dream about a statue of her husband that was full of holes that bled profusely. Fearing evil, she tried to convince Caesar that her dream was a warning for him not to go to the senate that day. Ceasar even has one of his servants go to the priests to do a sacrifice to see what they have to say about Calpurnia's fears. When the animal was sacrificed, there was no heart in it... a bad omen indeed. Caesar even ignores this omen when Decius Brutus re-interprets Calpurnia's dream to have a favorable meaning just to entice Caesar to come to the Senate (and to his doom).
Brutus' conscience conjours up the ghost of Ceasar who tells Brutus that he will see him at Philippi. Brutus is feeling guilty for his part in the conspiracy and his conscience manifests his guilt in the form of a ghost. It is at Philippi that Brutus meets his end, so the appearance of the ghost foreshadows his demise.