To what extent do the witches predictions dictate events in Macbeth? Are their prophecies binding?

To all the good answers posted above, I'll dare to add a few lines of my own about what my reading suggests.

The witches' predictions not at all dictate the events. Remember in the first scene of the first act, the witches say: "Fair is foul, and foul is fair". This statement of the weird sisters, for the first time, hints at how much ambiguity and dubiousness they are going to create in Macbeth's mind throughout the whole play. Ambiguity, or conflict between appearance and reality, is one of the key themes in this tragedy. The witches just equivocate in an ambiguous way, implying that, lie in a way which seems apparently true. And this they do solely to win his trust and make him a devil like them.

The witches know that, Macbeth is already an ambitious man who needs a spur in order to rouse his ambition and let it develop fully to achieve his end. They shows him what he wanted to see. They tell him what he wanted to hear. Their predicted apparent truth arises his inner demon and instigates his voracity. Macbeth is thus illusioned. He is told that no human born of woman can kill him, neither he would be killed till the Birnam Wood come close to his fort. Later, when he finds that the Birnam Wood does not come nearer, rather soldiers hiding themselves under leaves come closer, and Macduff is found to be born out of surgery probably because of his mother's illness or death, he understands clearly that, he has been deceived by the witches' dubious prophecy. In act 5, scene 7, disillusioned Macbeth tells to Macdufff:

"Accursed be that tongue... / That palter with us in a double sense, / That keep the word of promise to our ear/ And break it to our hope."

So, it is clear that, the witches prophesies contributes to influence and instigate him towards evil deed, but does not 'dictate events'.