This article is from the Tolkien Newsgroups FAQ, by Steuard Jensen firstname.lastname@example.org with numerous contributions by others.
The swords that the Hobbits got from the Barrow Downs were
apparently magical in some way: in "The Departure of Boromir", Aragorn
says this of Merry and Pippin's blades:
Doubtless the Orcs despoiled them, but feared to keep the knives,
knowing them for what they are: work of Westernesse, wound about
with spells for the bane of Mordor.
Some have objected that Men could not use magic "spells", as Tolkien
discusses in Letter #155: "'magic' in this story... is an inherent
power not possessed or attainable by Men as such." However, against
this in the margin Tolkien wrote, "But the Numenoreans used 'spells' in
making swords?" (and he omitted the whole discussion of magic from the
final version of the letter).
Some see the question mark in that margin note as an indication that
Tolkien was uncertain of this conclusion and look for non-magical
explanations for Aragorn's comment. However, most accept Aragorn's
statement as proof that the blades were magical (which we will assume
for the remainder of this discussion), and the remaining debate
concerns the nature of that magic.
There are several reasons to believe that the barrow blades were
particularly harmful to the Nazgul. A major piece of evidence is the
effect of Merry's blade on the Witch King, as discussed in question
III.C.4 (which should be read as part of this entry). A related quote
comes from Letter #210, where Tolkien compares that case to what would
have happened if Sam had "[sunk] his blade into the Ringwraith's thigh"
on Weathertop: "the result would have been much the same...: the Wraith
would have fallen down and the sword would have been destroyed." It
may be significant that Tolkien says "fallen down": he seems to think
that any stab (even an unskilled one) would have that effect (while not
slaying the wraith entirely).
In earlier drafts of LotR, it was explicit that the Nazgul feared
the barrow blades: in the chapter "At Rivendell" of _The Return of the
Shadow_, Gandalf refers to them as "the one kind of sword the Riders
fear." Although no such statement survived into the final text, some
believe that the Nazgul's fear of the barrow blades did remain.
Question III.C.3 discusses the possibility that the barrow blades were
part of the reason the Nazgul did not take the Ring at Weathertop (and
should also be read as part of this entry).
We know almost nothing about whether the barrow blades had any
special effect on other evil creatures. In "Flotsam and Jetsam", Merry
says that Ugluk (leader of the Uruk-hai band) took the swords but then
"threw the things away as if they burned him." However, this may just
be a poetic description of the normal fear mentioned by Aragorn in the
first quote above. In the end, no aspect of the barrow blades' magic
is well understood.