In Shakespeare's Macbeth, Macbeth himself tells the audience that his "vaulting ambition" is what pushes him forward—that and the ambitions of his wife.
There is no question that the witches' predictions strike a chord with Macbeth. The idea of being King appeals to him, though there is a great deal that stands in his way—first there is Duncan, and then Malcolm (the King's son) who Duncan names as his heir. Though he is the King's cousin, Macbeth is not next in line for the throne.
However, Macbeth wants to be King. Even when he hesitates because Duncan has been so generous in rewarding him for his efforts on Scotland's behalf on the battlefield, Macbeth allows his wife to shame him into pursuing the King's murder. She calls him a coward, but he tells her to be quiet: no one is braver than he is...
I dare do all that may become a man;
Who dares do more is none. (I.v.50-52)
When she finally convinces her husband to move forward with their plan, it is obvious he does not want to do it. First, he has many good reasons not to kill Duncan: he is Macbeth's King, his cousin, his friend, and his house-guest. Macbeth is not a murderer by nature. He has killed on the battle field, but not in cold blood. However, his ambition (as he noted) drives him on. Even seeing a "ghostly dagger" hovering before him on his way to the murder does not stop him.
We can see, however, how this terrible act (for which the Elizabethan audience believed he would go to hell—for killing a King) starts to change the noble man we met at the play's beginning. It's not just that he kills his King, but he begins to lose a sense of who he is—he is petrified to return the daggers to the scene of the crime:
I'll go no more:
I am afraid to think what I have done;
Look on't again I dare not. (II.ii.64-66)
This is at first encouraging in that we sense the honorable man inside him is fighting against what Macbeth has done. However, he notes that killing will probably get easier with practice—unfortunately, he is right. When the King's body is discovered, Macbeth pretends to lose his mind in his "grief" over Duncan's death by killing the guards who could expose Macbeth as the killer. From there, it only gets easier. He arranges for Banquo and his son Fleance to be murdered (though Fleance gets away); he also has Macduff's wife, children and servants slaughtered because Macduff turns his back on Macbeth and goes to Malcolm who is living in exile in England.
Ultimately, this course he embarks on also leads to Lady Macbeth's insanity when their actions become (ironically) too much for her to bear. Macbeth's ambition costs him a friend in Duncan and Banquo. He loses his sense of morality. He teeters on the edge of insanity. And he loses his wife to suicide. At the end, the only thing he has left is his refusal to run away or die a coward's death.
I will not yield,
To kiss the ground before young Malcolm's feet,
And to be baited with the rabble's curse.
… I will try the last. Before my body
I throw my warlike shield! Lay on, Macduff,
And damn'd be him that first cries, “Hold, enough!” (V.viii.32-39)
With everything else that ambition costs Macbeth, it ultimately also costs him his life.