The teaching materials available at eNotes have some excellent ideas for essays on this play. Check them out at the Lesson Plans link at the top of this page.
You might consider these topics:
- Some scholars think the play should be titled "Marcus Brutus." Explain why they say this.
- Analyze the character Cassius. Is he putting together the assassination plot for the good of Rome, or is he acting out of envy of Caesar?
- How might Rome have been different had Caesar not been killed?
- How does Shakespeare use foreshadowing to advance the plot?
That's just a few suggestions. I hope they help!