We know the story of when the people of Ta'if rejected the Prophet (peace be upon him), pelted him with stones, he was visited by the angel Jibril, and said - "here with me angel of the mountains, if you want, he will move them together, and this city is nothing left."
But the Prophet (peace be upon him) answered that it is not necessary to do it, if these people unbelievers, may be, their children will be believers. Character of the Prophet (peace be upon him) named in the Qur'an "Hulyukul azym" - his temper over the morals of others, that is, he seems to be the crown of all morality.
Scientists say that we shall not be obliged to curse even Iblis (the leader of the devils), for this, we will not be asked. We can only ask for protection from him.
So we must be careful in terms of curses and hold to it, thinking that there is something good, some merit. Some Muslims like to portray themselves of such cruel, harsh people, such pathos let in on themselves - "let them be cursed these misconceptions, these kafirs."
You should not curse unbelievers, you should make Dua to Allah, and that we were a good example for them (but ask God for forgiveness for the unbeliever is prohibited, in fact it's disbelief). This is the Dua of a true believer. A curse - a form of anger and aggression, it should be appropriate to the believer.