Many superstitions of the Elizabethan Age date back to much earlier times, including the Age of the Roman Empire.  Thus, the inclusion of omens and dreams in Shakespeare's Julius Caesar is of great significance both to the audience and to the play itself.  Throughout the play, there are soothsayers, dreams, ghosts, and personal interpretations of the stars that greatly affect the characters.

Caesar, of course, ignores all supernatural warnings and signs for fear that the Roman people think him weak.  He refuses to listen to the soothsayer who cautions him against the Ides of March; he ignores his wife's entreaties to not attend the Senate because she has had a most portentous dream.  The storm of the previous night moves him not.  All these signs he ignores lest his role as leader be questioned; yet, ironically, he is easily swayed by Decius's interpretations of these omens and dreams that he should, indeed, go to the Senate.

And, it is this vacillation between disbelief and belief that threads the play Julius Caesar.  For instance, in "the seduction scene" of Act I, Cassius tells Brutus,

The fault, dear Brutus, is not in our stars,

But in ourselves, that we are underlings. I,ii,140-141)

But later, in Act V, he tells Messala that he once "held Epicurus strong," meaning he does not believe, as Epicurus did, that the gods interest themselves in men's affairs.  but, now, Brutus says, "...I change my mind" (V,i,78-79). Cassius tells Messala of an omen that presaged death.

Likewise, Brutus vacillates between belief and disbelief in omens and other superstitions. For, in Act I, he is convinced by Cassius's statement that destiny lies in the hands of each man.  Later, he ignores the portents of the suicide of his wife Portia; however, he talks to Cassius of destiny regarding their forthcoming battle in Philippi:

There is a tide in the affairs of men

Which, taken at the flood, leads on to fortune;

Omitted, all the voyage of their life

Is bound in shallows and in miseries.

On such a full sea are we now afloat,

And we must take the current when it serves,

Or lose our ventures. (IV,iii, 244-250)

And, directly after this speech, Brutus encounters the ghost of Caesar, telling it,

That mak'st my blood cold, and my hair to stare?

Speak to me what thou art. ...

Ill spirit, I would hold more talk with thee. (IV,iii,315-317)

But when Cassius tells Brutus that "the affairs of men rests still incertain" after having witnessed the omen of the eagles, Brutus rejects such ideas saying,

But I do find it cowardly and vile,

For fear of what might fall, so to prevent

The time of life, arming myself with patience

To stay the providence of some high powers

That govern us below. (V,iii,112-116)

These words, indeed, echo those of Caesar before he goes to the Senate.  Is it, then, the ghost of Caesar which has made Brutus say these words--"thy [Brutus's] evil spirit"--or himself?

Certainly, from the opening festival of Lupercal in which infertile women hope to change their condition during this superstitious holiday, to the words of the soothsayer that presage the tragedy of Julius Caesar, superstition, along with its acceptance and rejection, is a powerful force in Shakespeare's classic play. But, perhaps like modern man, the Romans manipulated their superstitions to fit their own inner desires, fears, and motives, underscoring the statement of William Jennings Bryant:

Destiny is not a matter of chance, but of choice. It is not a thing to be waited for; it is a thing to be achieved.

And, so it is true, as Cassius says, that "the fault is not in the stars, but in ourselves."

Rome in Shakespeare's Julius Caesar is a superstitious place. 

Caesar demonstrates his superstitious beliefs when he arranges for Antony to touch the barren Calphurnia while he runs the race in Act 1, because superstition suggests that the touch may cure Caesar's wife of her inability to have children. 

Caesar makes the mistake, however, of ignoring superstition when he fails to follow the Soothsayer's advice to beware the ides of March. 

Furthermore, the chaotic state of human affairs in the play is reflected by bad omens.  A slave's hand appears to be consumed by fire one minute, but not at all burned the next.  A lion is loose in the city by the capitol.  Caesar's ghost appears to Brutus on the eve of battle. 

Superstition in the play reflects the state of Roman politics, highlights Caesar's refusal to accept advise and accept his fragility, and foreshadows events to come. 

In the play "Julius Caesar" by William Shakespeare, the author combines two very interesting and contrasting ideas. The first is the Roman civilization with it's logical and practical way of accomplishing projects of epic proportions - a method based on fact and cold analysis. The second idea contrasts this sceptical and logical society with the idea of imagination and surmise or superstition and fear - an idea the Romans couldn't quite let go of when they beheld it in the peoples they conquered. The Romans would leave nothing to chance and preferred to have all bases covered - even if there was nothing in the native religions or superstitions. So in "Beware the ides of March" we have a soothsayer trying to warn Caesar that bad things might happen if events were scheduled on a certain day. The Muslim festival of Ide at that time is worth researching too.