Author's note: I do not own Lord of the Rings or any of the related works. Don't sue me for using them.
The Witch King didn't often feel pain. He didn't often feel anything, other than the pull of the Ring and the will of his Master.
Sure, during the war there had been elves and men who hadn't run from his very presence. They had cut him. But most of those had been normal, nonmagical blades, unable to hurt him at all. Even the magic blades had barely slowed him down - because no man could kill him.
So, one day, the Witch King was rather surprised when he felt something akin to a pinprick on his leg. His senses, such as they were, indicated that there wasn't anything nearby. Nothing that wasn't under his command, at least. Certainly nothing capable of hurting him.
However, it had only been a pinprick. It wasn't anything to worry about.
The following day, the Witch King began feeling hot. This was unusual, because he was more of a spirit than anything, and as such was more or less immune to temperature.
Still, the Witch King was unconcerned. He put it down to his Master rising in the east. Perhaps he was working some great spell. After all, if no man could kill him, why should he be afraid of anything?
Later, the Witch King began feeling cold. Shivers ran through his ethereal body. Which was impossible. Nothing could affect him like this! He was the Witch King!
Later still, the Witch King died, his body (such as it was) dispersing like mist under the sun. His last thought was "Impossible! I cannot die! I ca-"
A long way away, Radagast the Brown held out a hand. A larger-than-average mosquito landed upon it. Radagast stroked it gently with a finger, proud of his creation.
The Witch King couldn't be killed by any man. However, only female mosquitos bite people. It had been simple enough for Radagast to engineer a little magical disease for his mosquito to carry. The Witch King hadn't suspected a thing.
So it was that the Witch King died, and the inhabitants of Middle Earth learned not to mess with Radagast.