What is an example of a person vs. supernatural conflict from Julius Caesar?

The play contains many examples of superstitions and warnings of doom. 

A person vs. supernatural conflict is a conflict between a character and something that is not normal in some way.  Supernatural elements include ghosts, omens, and superstitions.  Romans were very superstitious, and there are many examples of superstitions in the play.

First of all, the soothsayer’s warning to Caesar is an example of a character vs. supernatural conflict because the soothsayer warns Caesar that he is doomed.  Caesar does not pay attention, even though someone is telling him a specific day when he should beware. 

CAESAR

What say'st thou to me now? speak once again.

Soothsayer

Beware the ides of March.

CAESAR

He is a dreamer; let us leave him: pass. (Act 1, Scene 2) 

This is not the only bad omen mentioned in the play.  The conspirators mention all kinds of spooky signs that they say they saw, such as tempests, flaming slaves, and owls during the day.  Calpurnia has a dream where she imagines Caesar’s blood running like a fountain, and she does not want him to go to the capital on the Ides of March.  Caesar almost listens to her, until Decius Brutus convinces him to reinterpret the dream as a positive sign.  Of course, it wasn't.  Caesar was assassinated on the Ides of March.

Another example of a character vs. supernatural conflict is Cassius’s birthday omens.  Cassius gets very superstitious on his birthday, deciding that the bad omens he is seeing mean that his battle is doomed and he is about to die.  Although Cassius says he does not normally pay attention to omens, the combination of the fact that it’s his birthday and he is about to go into a battle he does not think will go well makes him morbid.

Coming from Sardis, on our former ensign
Two mighty eagles fell, and there they perch'd,
Gorging and feeding from our soldiers' hands;
Who to Philippi here consorted us:
This morning are they fled away and gone;
And in their steads do ravens, crows and kites,
Fly o'er our heads and downward look on us,
As we were sickly prey … (Act 5, Scene 1)

Cassius was right to be worried.  Brutus and Cassius were apparently outmatched at Philippi.  Cassius’s interpretation of the omens led him to misread what happened in the battle and commit suicide prematurely.  Brutus’s suicide came not much later.