Brutus decides to join the conspirators not because of something that Caesar has done but because of what Cassius suggested Caesar might do, which prompts Brutus's soliloquy in Act 2.1. Here he weighs his personal knowledge of Caesar's character against the way Caesar may change if he is crowned ("I know no personal cause to spurn at him / But for the general. He would be crowned: / How that might change his nature, there's the question" (2.1.11-13). And then, with Cassius's suggestions in the back of his head, he decides Caesar might abuse his power and should therefore be murdered. Referring again to Iraq (and perhaps even to Iran), statesmen often make decisions with horrific consequences based not on what has happened but what might happen, a sort of "preventive" or "proactive" approach. Our political pundits are now constantly debating this issue in regards to our invasion of Iraq and of handling of diplomacy (or lack of that) with Iran, considering if it is right for America to make decisions based on what a country might do rather than what it has done.
If you are looking just at the character of Caesar, I think his ambition is something that relates to today and to all people in general. Brutus fears that Caesar's ambition will lead him to become corrupt and, eventually, a dictator of Rome. I think people today can relate to being ambitious. Who among us wouldn't like to make the most out of our station in life? Is Caesar so different? He is murdered because he might become corrupted by his power. I think if you look around at politicians, leaders, and even celebrities, you can easily see corruption at work and how it can ruin a person.
Another interesting aspect of the play that really is applicable to our society today is the fickleness of the crowds. One minute they are all for Brutus and the conspirators' decision to murder Caesar. Then Anthony speaks to them after Brutus, and he quickly turns them against the conspirators and the crowd runs off in a mob. Look at how quickly people are persuaded today via the media. Before the war in Iraq, look at how many people thought there were really weapons of mass destruction there. But the masses were deceived. You could argue that the people today are even more fickle than the Romans in Shakespeare's play.