Macbeth demonstrates his self-awareness throughout the play, beginning in Act I, Scene 4, when he says, "Stars, hide your fires; Let not light see my black and deep desires." He recognizes that his ambition to be king by killing Duncan would be an indefensible and immoral act, yet his thoughts drift to that place.
Another quotation that demonstrates Macbeth's self-awareness is found in Act I, Scene 7, when he observes "I have no spur/ To prick the sides of my intent, but only/Vaulting ambition." What Macbeth means is that he has no legitimate reason to commit regicide; Duncan is a fine king with integrity and a loyal following. He admits that the only reason he wants to kill Duncan is because he wants the throne for himself.
Another example is found in Act I, Scene 7, when Lady Macbeth questions her husband's masculinity. He answers her briefly and without apparent heat: "I dare do all that may become a man;/ Who dares do more is none." Here, Macbeth is solid in his self-awareness as a man; he is, after all, a heroic soldier who has just dispatched rebels in the name of Scotland.