At the top of my "never want to visit list" used to be Hawaii, which is, of course, actually a state not a country. As a child, for some reason I was under the impression that Hawaii was one of the hottest places on earth. I have since learned that it actually has a fairly mild climate. Another reason that I didn't want to go there, though, was because it is such a popular tourist destination. I'm often more interested in places that are less popular.
I'm not sure I have any that I absolutely would not visit, but as others have mentioned, personal safety would be a deciding factor. Some countries may not be safe to visit right now, but could be perfectly safe in 5 or 10 years. For instance, I visited Ukraine 15 years ago and it was safe then, but it might not be such a safe place now. In the same manner, Ireland wasn't so safe in the 90's, but is a very safe place to visit now.