As I understand it, Shakespeare's Julius Caesar is often treated as a history, much like his Richard and Henry kingship plays. However, it seems to me (from the little research I've found) that it is more likely a heavily fictionalized tragedy along the lines of Macbeth or Hamlet. Or is it somewhere in between, a mixture of semi-accurate history and hyperbolic or even outright fictionalized drama?
Shakespeare reworked Plutarch's and Suetonius' accounts, with considerable amount of his own innovations stuck in. Neither Plutarch nor Suetonius, for example, has Brutus and Cassius visited by Caesar's ghost before the Battle of Philippi. The speeches are all unique to Shakespeare.
Courtesy of the University of Chicago's website, here's an excerpt from Plutarch's Life of Marc Antony regarding Caesar's funeral.
From such considerations as these, however, he was soon shaken by the repute in which he stood with the multitude, and he had hopes that he would surely be first in the state if Brutus were overthrown. Now, it happened that when Caesar's body was carried forth for burial, Antony pronounced the customary eulogy over it in the forum. And when he saw that the people were mightily swayed and charmed by his words, he mingled with his praises sorrow and indignation over the dreadful deed, and at the close of his speech shook on high the garments of the dead, all bloody and tattered by the swords as they were, called those who had wrought such work villains and murderers, and inspired his hearers with such rage that they heaped together benches and tables and burned Caesar's body in the forum, and then, snatching the blazing faggots from the pyre, ran to the houses of the assassins and assaulted them.
Note that Plutarch indicates that there's a major speech that turned the masses against the liberadores and towards the Caesarians, but he does not have Antony give a speech starting "Friends, Romans, Countrymen."