An equivocator is someone who lies and tells half-truths, or says something ambiguous to mislead another. In Shakespeare's play, Macbeth, the witches are generally considered the "great" equivocators in the play in the play. (In the second set of predictions they deliver in Act Four, they tell half-truths to trick Macbeth.) However, we can see instances, also where Macbeth is no better than the witches for telling lies.
The first instance where Macbeth outright lies is when he says he killed Duncan's guards because he was so upset over Duncan's murder at their hands. He actually kills them so they cannot raise doubts in anyone's mind that they were "framed."
O, yet I do repent me of my fury,
That I did kill them. (II.iii.117-118)
He excuses his behavior, wondering how anyone could be levelheaded in the face of such horror: seeing his beloved King murdered.
Another instance is when Macbeth speaks to Banquo, ostensibly to ask him if he will be gone long when he goes riding—to remind him not to be late for dinner because Macbeth wants to speak to him. Macbeth is actually making plans to have his friend murdered because Banquo heard the witches' initial predictions that told Macbeth he would be king, and Banquo has told Macbeth that he will not be swayed from what he believes to be morally correct.
We should have else desired your good advice,
Which still hath been both grave and prosperous
In this day's council; but we'll take tomorrow.
Is't far you ride? (III.i.23-26)
Later in the same scene, Macbeth meets with the men he has hired to murder Banquo. They are not professional killers, but simply common men whose lives have taken a turn for the worse. Macbeth has told the men that Banquo is to blame for their dire circumstances—when they had originally thought it was Macbeth. (The truth is that it was Macbeth who had beggared them.)
That it was he, in the times past, which held you
So under fortune, which you thought had been
Our innocent self?
...“Thus did Banquo.” (81-84; 89)
Macbeth goes on to ask these men (much like his wife asked him with regard to Duncan) if they are kind-hearted enough to ignore what Banquo has "done," or if they will be man enough to do something about it.
Of course, the men believe Macbeth (as most of his peers do at the beginning), never expecting that this new King of Scotland is lying to them. He tells them that he could kill Banquo easily himself, but that he doesn't want to offend important men who are mutual friends to Macbeth and Banquo.
Macbeth does all he can not only to take the throne from Duncan, but to make sure it remains in his possession.