The main reason why there are still nuclear weapons is that it is impossible to un-invent them. If one side has them, then, by definition, the other must have them as well. The more countries that posses nuclear weapons, the more difficult it because to disarm; nuclear weapons are the great equalizer: they allow a smaller nation to stand up to a more powerful one.

Furthermore there are certain high-value targets that in case of a general war can only be destroyed with nuclear weapons, there simply isn't any alternative.

Finally, the military from various countries have been studying the possibility of destroying or deflecting asteroids and comets in case they should be a collision course with Earth. NASA has fielded some alternatives but none of these can actually be implemented in the short time we would have to deal with this kind of threat.