What is the climax in Macbeth?

The "climax" of a story is the part at which the tension is ratcheted to its highest point. It can sometimes describe a crisis point which precipitates the falling action to follow. In a tragedy, the climax is usually the point at which the hero is no longer able to continue fighting against his fatal flaw, and it begins to destroy him—things start to unravel after the climax, effectively.
In Macbeth, then, we find the climax in act 3, scene 3. Macbeth has carefully planned, or so he thinks, for Banquo to be murdered. Unfortunately, while the murderers manage to kill Banquo, Fleance escapes; as the second murderer says, "We have lost / Best half of our affair." As we know, the real threat to Macbeth as king is Banquo's "issue"—his children. In allowing Fleance to escape, then, the murderers have indeed failed to carry out Macbeth's plan. After this point, Macbeth is no longer able to keep up with all the threads he is trying to control, and the falling action of the play begins.
I would note that asking "what is the climax of the play" is not a question to which there is one definitive answer. Shakespeare did not write the play using a paint-by-numbers approach to plot structure, and some have argued that the murder of Duncan in act 2 is the climax, or the fight between Macbeth and Macduff. For me, however, I think the murder of Duncan comes far too early in the play to constitute the climax—the tension continues to rise after this point as Macbeth pursues the plan that the murder of Duncan has set in motion. Meanwhile, the fight between Macbeth and Macduff seems to me rather the end of the falling action and the beginning of the denouement, according to Freytag's pyramid model of plot structure. It is in act 3, scene 3, that the climactic tension is punctured by the failure of the murderers to kill Fleance, after which point the audience knows that surely everything must now go wrong for Macbeth.