We may be able to argue that Julius Caesar is a representative character, symbolic of the same flaws demonstrated by each and every one of the politicians in the play. He is ambitious, a trait which leads to his downfall (like Brutus and Cassius). He desires greatness for his country, but only through himself, insisting on placing himself in the center of every decision (like Antony).
So, even if the play doesn't feature Caesar as a character, it is his character that the play explores, if symbolically and obliquely.
Julius Caesar is known as one of the most powerful and influential leaders ever. Even the word "Czar," meaning leader, is a derivative of his name. Caesar is so powerful that even after his death his influence continues to reside in all the characters. Antony and Octavius waged a civil war in Rome under his name. As he was dying, Cassius paid homage to Caesar declaring him the victor. Brutus was so preoccupied with Caesar, even after his death, that he imagined confrontations with Caesar's ghost. If Caesar was killed in Act II and never mentioned again, I'd say it is an unfitting title, but since his influence continued on throughout the play and beyond, I find it quite appropriate.
That Julius Caesar's character is pivotal to the entire play is evinced in the influence of his looming ghost which even appears one time to Brutus. For, having slain Caesar, the three main characters undergo certain transformations that are imitative of Caesar himself. First, Marc Antony, like Caesar who eliminated his ally Pompei, dispenses with his nephew, Publius, as "a slight unmeritable man." In Act V, he argues with Octavius, again displaying almost a sickness of the mind suggestive of Caesar's "fallings down." Then, Brutus, like Caesar who refused to listen to the soothsayer and the warnings of his wife Calpurnia, refuses to consider the advice of Cassius not to allow Marc Antony to speak before the Romans. Cassius also cautions Brutus in Act IV to let their troops rest and force the enemy to march to them at Philippi, but Brutus contradicts him in Caesarean fashion,
There is a tide in the affairs of men
Which taken at the flood, leads on to fortune....
Finally, Cassius is affected by Caesar's ghostly effect as he becomes, like Caesar, superstitious in Act V as he tells his friend Messala that he is convinced that they are going to lose the battle because he has seen signs such as two eagles swooping down upon the soldiers as "sickly prey."
Julius Caesar may not be bodily present throughout much of the play, but his death is a catalyst for the remaining action, and his ghost looms closely over the souls of those involved with his slaying and the future of Rome.
I agree with other posters in the way that the death of Caesar actually foreshadows the death of other crucial characters in the play, most importantly Cassius and Brutus. Whilst Caesar only occupies roughly the first half of the play, let us not forget that his spirit lives on, especially in the appearance of his ghost to Brutus.
The play is aptly titled Julius Caesar because everything that occurs and every downfall of every person is predicated (i.e., founded) upon Caesar's existence and power. Thus his death is the means to the end; it is the compelling reality in the play. Plus, his presence is felt throughout and influences how the other characters perceive and what they do.
Very simply, Julius Caesar is aptly named because Caesar is the tragic hero of Shakespeare's play; therefore, this particular tragedy could have no other name. Similar to Macbeth, Caesar's tragic flaw is ambition. He is a generally noble character whose downfall was brought about by a tragic flaw that he realizes far too late (moment of catharsis being "Et tu, Brute?"). The play must go on, of course, to have this tragedy (as Aristotle would say) end on a note of hope.
I believe the full name of the play is The Tragedy of Julius Caesar, and that it fitting since Caesar was the main character. While Caesar is only physically in part of the play, there would be no tragedy if Caesar had not become overly ambitious. He would not have needed to be stabbed, thirty-three times. After his death, his ghost haunted Brutus so he did continue to be a part of the play.
Also, there would have been no conspirators if Caesar had not become overly ambitious. If Caesar had not been a threat to Rome's security, there would have been no tragedy.
While Brutus does seem to be a main character, he is only important to the play as a conspirator who killed Caesar for the good of Rome. Even Brutus loved Caesar, but he loved Rome more. Caesar had become too ambitious. He was a threat to the freedoms of Rome's Republic. Brutus was afraid that Caesar was becoming a tyrant. The play revolves around removing Caesar from power.
Since Brutus was such an honorable man, he would have never agreed to the murder if Caesar had not been a threat. Brutus would have never become part of such a conspiracy had he not feared for Rome's safety. Truly, Caesar had determined to crown himself King:
Caesar has become the most powerful man in the Roman Republic and is eager to become king.
For this reason, Caesar, in all his ambition, is the main reason for such a tragedy, thus we have a play detailing his murder. The conspirators had no idea the remaining play would need to have been written. They did not plan on fleeing for their very lives.
Caesar, though not nessissarily the main character, is the one who instigates everything that happens. If not for him, then Brutus would not have had this secret to keep, the conspiracy would not have happened, the fight would not have happened, etc. If he had not existed, things would have been completely different, and there would be no story.