In Shakespeare's Julius Caesar, was Caesar ambitious?

In Shakespeare's Julius Caesar, the title character, Caesar, is indeed ambitious. The play begins after a civil war, the victor of which, Caesar, is the most powerful man in Rome and poised to become the king (or dictator, to be more accurate). The play begins with characters, especially Brutus, worrying about Caesar's ambition, and this worry ultimately drives the conspirators (Brutus among them) to assassinate Caesar. Though Antony throws doubt on Caesar's ambition during his funeral speech in Act 3, Scene 2, he does so to pursue his own political motive. As such, we can view his implied assertion that Caesar was not ambitious as an intentional lie. 

The problem of Caesar's ambition makes more sense when remembered in its historical context (the play is a fictionalized retelling of real events, after all). Prior to Caesar's rise to power, Rome had been a republic for hundreds of years, governing its people through representative government, rather than a monarchy. Thus, Caesar's personal ambition to gain power as king threatens this democratic status quo. As such, Julius Caesar is a play about how personal ambition, when it is paired with political power and motive, has the potential to threaten the sovereignty of self-governance.