The accepted wisdom is that Eowyn and Meriadoc killed the Witch-king on the Pelennor Fields. However a close reading of The Return of the King can support a different hypothesis that he did not die at that time, and that it was only Meriadoc who dealt significant damage.
Meriadoc struck him in the back of the knee, a feat made possible because of his sword; “No other blade … would have dealt … a wound so bitter, … breaking the spell that knit his unseen sinews to his will.”
This wound caused him to stumble in pain; so physical dissolution was not instantaneous. Merry had time to call Eowyn's name twice, and she had time to struggle from her knees and strike with her sword at his head, while the wraith remained bent over in bitter pain. Her sword shattered, so it must have encountered some aspect of the Witch-king's powers and at that moment the crown fell to the ground, and his body was gone. Did Eowyn's blow instantaneously dismiss the wraith, or was this just a co-incidence of timing? He did not necessarily die at that time either; his voice “was never heard again in that age of this world” (Referring to the Third Age, which finished only a few years later when the Ring-Bearers sailed into the West). A possible implication is that his voice was heard again in a later age, although the destruction of the One Ring would have made further survival of the Wraiths difficult to say the least, especially given that they were originally Men (albeit probably Second Age Numenoreans, and therefore very long-lived).
An aside into the protective prophecy; given in The Return of the King as “no living man may hinder me” (The Witch-king) or “not by the hand of man shall he fall” (Gandalf), but the original prophecy by Glorfindel at the Battle of Fornost was “not by the hand of Man shall he fall”. But both Eowyn and Meriadoc were of the race of Men (Hobbits being an accepted but not explicitly cited sub-branch of the race), and Meriadoc was male as well. The most obvious reading of the events of the battle is that Eowyn's blow caused his death by sole virtue of her being female; this appears to have been viewed as plausible by the Witch-king himself at the time. But Glorfindel's specific reference to the Race of Men does not support this.
Meriadoc's Westernesse sword was uniquely capable of causing severe damage to the witch-king, and was explicitly credited with causing physical dissolution, even though Glorfindel's prophecy should have precluded this; so either the prophecy was inaccurate, or he did not “fall” at that point in time, and was only temporarily defeated. In either case it is unlikely that Eowyn's blow was effective, it was simply co-incident with the destruction of the Witch-king's body by Meriadoc.
References for this hypothesis;
I have posted this to the Talk page of the Wikipedia entry for the Witch-king, where hopefully someone better versed in Tolkien mythology may have some constructive criticisms!