Macbeth is responsible for the killing of King Duncan, and then Lady Macbeth is next in line for the responsibility because she prodded him along.  What the witches did was light the flame, but they cooked with it.  The witches influenced Macbeth, but if he had not already been thinking along those lines it never would have gone that far.

The above commentators contradict with each other on whether the three witches are responsible for the murder of Duncan. Macbeth’s comment in Act I, Sc. iii must be taken into account in this case: “This supernatural soliciting / Cannot be ill; cannot be good: […] / If good, why do I yield to that suggestion / Whose horrid image doth unfix my hair […]?” This clearly demonstrates that Macbeth has been greatly influenced by the “supernatural soliciting” of the three witches. Later in Act I, Sc. v Macbeth says: “Let not light see my black and deep desires”. The “suggestion” (of becoming the king) Macbeth refers to in Act I, Sc. iii can be connected to his “black and deep desires” (to kill Duncan and become the king), referred to in Act I, Sc. v. This clearly shows that Macbeth’s desire to kill Duncan has been directly influenced by the prophecies of the three witches and based on this observation it can justifiably be said that the three witches are directly responsible for the murder of Duncan.

On the other hand, the three witches ARE responsible for the death of King Duncan.  Macbeth has no plans to kill the king or wishes for the King's death until seeing the prophecies of the witches.  Had the battle against Norway ended and Macbeth and Banquo gone home without seeing the witches, King Duncan probably would not have been killed.  Upon learning that the second prophecy was true, then Macbeth began considering the third prophecy.  In fact, even upon hearing the prophecy for the first time, Macbeth replies by saying, "to be king stands not within the prospect of belief."  Then, after learning of his new title, he says,"Glamis, and Thane of Cawdor! The greatest is behind."  If the witches wouldn't have said anything to Macbeth, he probably wouldn't have even considered becoming king. 

So are the witches responsible?  I think yes they are; cmcqueeney says no.  The greatest part about literature, though, is that you get to decide for yourself what you believe.

The three witches are not responsible for the murder of King Duncan.  They prophesy that it will happen, but they do not make it happen.  Macbeth's choices cause the death of the King.  This play brings up the debate of free will vs. fate, but Shakespeare seems to support free will ruling over fate.  If you read over the enote commentary from Act I, linked below, you will see some of the specific lines that point to the limitations of the witches power and the power of free will. 

In Shakespeare's Macbeth, do the witches influence Macbeth's decision to commit murder?

This questions involves two of the most important themes of Macbeth, free will and supernatural intervention (or fate.) Shakespearean scholars disagree on the degree to which the witches are complicit in the murders. It is clear that they mean to manipulate Macbeth to do evil deeds, as Hecate makes clear in her speech in Act III, Scene 5. She says that she:

Shall raise such artificial sprites 
As by the strength of their illusion 
Shall draw him on to his confusion. 
He shall spurn fate, scorn death, and bear 
His hopes ’bove wisdom, grace, and fear. 
And you all know security
Is mortals’ chiefest enemy.

In many ways, this describes the witches' approach to dealing with Macbeth. They do not actually influence events directly, but rather manipulate Macbeth. In the first meeting, the witches only prophesy the future when they tell him that he will be king. They do not even suggest murder, much less tell him how to proceed. It is up to him to make that happen, or choose to wait for it to happen. Once Macbeth has begun to think about murdering Duncan, it is his wife that pushes him along to carry out what he is resolved to do. But it was ultimately his idea, neither the witches, by piquing his ambition nor his wife by steeling him for the task of murder, made his decision for him.