In the Lord of the Rings when the Lord of the Nazgûl is killed, there seems to be some confusion as to exactly who is responsible? Is the reason down to the sword of the Barrow Downs that Merry stabs him with, or does this simply make the Nazgûl vulnerable to normal weapons? The book seems to indicate that it is a combination of the sword strikes from Éowyn and Merry and that both were necessary for his demise (that is just my interpretation of how things are written). The prophecy that he cannot be killed by the hand of mortal man is not much help in explaining this since neither Éowyn nor Merry is a man!
There's no doubt that Eowyn's was the killing blow. There is however some debate about the exact role played by Merry - and, in particular, Merry's sword. Here's the key passage:
So passed the sword of the Barrow-downs, work of Westernesse. But glad would he have been to know its fate who wrought it slowly long ago in the North-kingdom when the Dûnedain were young, and chief among their foes was the dread realm of Angmar and its sorcerer king. No other blade, not though mightier hands had wielded it, would have dealt that foe a wound so bitter, cleaving the undead flesh, breaking the spell that knit his unseen sinews to his will.
This seems to hint that it was the sword, not the wielder, which undid the spell that made the Witch-King invulnerable. But it also makes it clear that that blow was key to enabling Eowyn's killing stroke. So, would a Man have been able to strike that same blow, if he had happened to be there holding the same sword?
I'm inclined to think that the question is moot. The prophecy was not "no man can kill me", it was "not by the hand of man will he fall": Glorfindel, making the prophecy, was just foreseeing that it would be not be a man who would wield the sword. And both Merry and Eowyn fit that description.
It's reasonable to assume that Eowyn's was the fatal blow - after all, the death cry and passing away immediately follows her blow. There's a fairly strong cause and effect there.
However we do know the Barrow-blade has special anti-Ringwraith properties as mentioned in the Return of the King:
No other blade, not though mightier hands had wielded it, would have dealt that foe a wound so bitter, cleaving the undead flesh, breaking the spell that knit his unseen sinews to his will.
Sam does not 'sink his blade into the Ringwraith's thigh', nor does his thrust save Frodo's lift. (If he had, the result would have been much the same as in III 117-20: the Wraith would have fallen down and the sword would have been destroyed.)
And in an essay (The Hunt for the Ring) reproduced in The Lord of the Rings: A Reader's Companion.
[Frodo] had dared to strike at [the Witch-King] with an enchanted sword made by his enemies long ago for his destruction. Narrowly it had missed him. How he had come by it — save in the Barrows of Cardolan. Then he was in some way mightier than the B[arrow]-wight; and he called on Elbereth, a name of terror to the Nazgûl. He was then in league with the High Elves of the Havens.
Escaping a wound that would have been as deadly to him as the Mordor-knife to Frodo (as was proved at the end), he withdrew and hid for a while, out of doubt and fear both of Aragorn and especially of Frodo.
Another key bit of information is that Merry does only stab the Witch-King in the back of the knee in the Return of the King:
Merry's sword had stabbed him from behind, shearing through the black mantle, and passing up beneath the hauberk had pierced the sinew behind his mighty knee.
I think the combination of the location of the wound and Tolkien's note in letter #210 indicate that Merry's wound would not have been fatal on its own. If Merry had pierced the Witch-King's heart, the story would have been different as the Hunt for the Ring notes indicate - that would have been a fatal wound. As it stands, instead the wound Merry inflicted was especially painful because of the nature of the sword and acted as a great distraction, allowing Eowyn to deal the fatal blow.
It's not detailed as such, but combining the above quotes I read it as implied that Eowyn could have dealt the fatal blow on her own if she had had the opportunity, but without Merry's actions she probably would never have got such an opening and instead died on the Fields of Pellenor. However it's definitely open to other interpretations.
I will add to the other (correct!) answers this detail from Appendix A (II THE HOUSE OF EORL, Third Line):
In that day Éowyn also won renown, for she fought in that battle, riding in disguise; and was known after in the Mark as the Lady of the Shield-arm.(1)
(1) For her shield-arm was broken by the mace of the Witch-king: but he was brought to nothing, and thus the words of Glorfindel long before to King Earnur were fulfilled, that the Witch-king would not fall by the hand of man. For it is said in the songs of the Mark that in this deed Éowyn had the aid of Théoden's esquire, and that he also was not a Man but a Halfling out of a far country, though Éomer gave him honour in the Mark and the name of Holdwine. [This Holdwine was none other than Meriadoc the Magnificent who was Master of Buckland.]
So we have that "in this deed" she (not a man) was aided by Merry (not a man). This deed being the fall of the Witch-king, this passage confirms that Éowyn was the final responsible.