This article is from the Tolkien Newsgroups FAQ, by Steuard Jensen firstname.lastname@example.org with numerous contributions by others.
Most agree that Eowyn's stroke was the immediate cause of the
Witch-king's death: she certainly struck _something_, and his death cry
and disappearance followed immediately after her blow. The primary
debate is whether Merry's role was simply to provide a distraction, or
whether his sword (taken from the Barrow Downs) was necessary to break
some "spell of protection" that would otherwise have guarded the
Witch-king from harm.
Question III.C.2 discusses the (possible) magical nature of the
hobbits' barrow blades and their effect on the Nazgul. In the context
of Merry's encounter with the Witch King in "The Battle of the Pelennor
Fields", the crucial statement is that
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.
(See question III.C.2 for a related quote and further discussion.)
Most (but not all) read this quote as a direct statement that Merry's
sword was especially harmful to the Nazgul. It is less clear what
"spell" is being broken: some read this as a poetic description of a
(nonmagical) collapse due to (possibly magical) great pain, while
others take it to mean that the Nazgul had only indirect, magical
control over their physical bodies. Based in part on this quote, some
go even farther and suggest that the Witch King was immune to physical
weapons before being hit by the barrow blade. No clear answer is