This is a good question. There are several very important incidents in the play Julius Caesar.
First, there are many religious incidents that are important. The words of the soothsayer - beware the ides of March - and Caesar's disregarding of these words are significant. This shows that Caesar might be filled with hubris. The same can be said when his wife asks him not to go to the Senate on account of a bad dream.
Second, another key incident in the play is when Cassius persuades Brutus to join the conspiracy. To have Brutus on board makes the conspiracy more noble, because Brutus is an honorable man and one who is synonymous with the Republic.
Third, another key incident is when Antony is allowed to give a speech during Caesar's funeral. Through his speech, especially his use of the word, "honorable," he is able to turn the Romans against the conspirators.
Finally, the death of the conspirators and the rise of Octavian is significant, as this shows the end of those who killed Caesar, but also the rise of Octavian, who will later be called Augustus.