Caesar lives on after his death in many ways.
1. He wisely set up his will before his death, and designates his nephew, Octavian, who is also his adopted son, as his heir. While Octavian might not have been the people or Senate's first choice as successor, they still want to honor Caesar; so the manner of his death encourages them to be even more vigilant in carrying out his wishes.
2. In Caesar's will, he also leaves money to each Roman citizen and park locations. Antony uses this information when he tantalizes Caesar's funeral crowd with the reading of the will. After the crowd hears that "their" Caesar thought of them even after death, they turn against the conspirators with whom they had sided just minutes before Antony's speech.
3. In the play, Julius Caesar, Caesar's ghost comes back to "haunt" Brutus, and actually provides a warning to him about the upcoming battle.
4. In history, Caesar has left an indelible mark even after death. His battle strategies are still studied at military schools (he never lost a single battle). Following heirs to the Roman Empire were named "Caesar" after him, and other world leaders followed suit ("czar," the former term of leadership from Russia comes from Caesar's name).