Caesar is just casually talking with his friends and followers. Someone starts yelling his name and calling out for him and Caesar asks who is calling on him. A Soothsayer yells, "Beware the ides of March." (I:II:ln 18) This is important because it foreshadows what's going to happen later on in the story. Although, Caesar doesn't believe him and ignores it and goes on, he tells him to beware because of what will happen later in the story.
Act IV: SC III
The conspirators go to Brutus' house in attempt to get him to join the conspiracy. Once they talk, he agrees although he doesn't come right out and say it. In agreement Brutus says, "Give me your hands all over, one by one." (II:I:ln 112) This is a big part in the story because it's when Brutus decides to go against Caesar and when the problem really begins for the story.
Act V: Sc V
The Conspirators enter the capitol to find Caesar. When they do they follow out their plan and then Casca says, "Speak hands for me!" (III:I:ln 78) This is basically their signal to stab Caesar, which they start doing. This kills Caesar. This is probably the most important part of the story because it's the turning point and the main character dies. Without this part the whole story would be pointless.
THEME: Act IV: Sc III
Brutus and Cassius goes into Brutus' tent to fight about why they've been cold to each other. They say how they wrong each other and Cassius even offers to let Brutus murder him. Before this Cassius says, "You wrong me in every way; you wrong me, Brutus." (IV:III:ln 55) This just shows how self-destructive they are and how they let their emotions get in the way. It's a way of showing they don't have what it takes to be rulers of Rome.
Brutus finds a friend (Strato) finally, that will hold a sword so he can kill himself. He kills himself because he's losing the battle and he says it's his time. As his final words Brutus says, "Farewell, good Strato." as he runs on his sword, "Caesar, now be still; / I killed not thee with half so good a will." (V:V: ln 50-51) This is pretty much the last big event before the story ends, without it, it wouldn't be clear who won the war. It's how the problem is resolved.
People are masters in their own fate. I believe in the story this is a huge theme, they pick their own fate in everything they do by the choices they make. In the story Brutus says, "There is a tide in the affairs of men / Which, taken at the flood, leads onto fortune; / Omitted, all the voyage of their life / Is bound in the shallows and in misery." (IV:III:ln 217-220) When Brutus tells Cassius this, he's leading himself to his own death.