A prophecy
"He will not return to this land. Far off yet is his doom, and not by the hand of man will he fall." —Glorfindel, The Return of the King, Appendix A (iv)
has been interpreted by many to mean "no man" could kill the Witch-king of Angmar.
I was thinking about the battle on Weathertop when Strider fought the Nazgûl with sword and fire to save Frodo. I'm pretty sure there were a few Nazgûl missing during the attack, and I'm not positive that the Witch-king himself was there, but it made me wonder if any of the other eight Wraiths could be destroyed by man? Strider, with all of his skills, didn't kill a single one.