The Witch-king perceived that Wormtongue was evil and that he would harm Saruman. That is why he let Wormtongue go, instead of killing him. However, it probably didn't take a genius to see that ...

Now, the Witch-king of Angmar is a pretty mysterious figure in the source material, and his true identity is never revealed. What we do know about him, though, is that he's Lord of the Nazgûl and ...