The Cold War is over. There is no need for nuclear weapons. Russia and the United States need to decommission their stockpiles of weapons for peaceful uses. The world learned its lesson when the two superpowers came to near Armageddon on a few occasions. The lessons of history cannot and will not be forgotten.
I don't believe that a world without nuclear weapons will ever happen. Some countries will always be trying to take part in nuclear programs and make nuclear weapons. Some countries are ran by dictators like Iraq was. The United States believed they were trying to gain nuclear weapons for future use and that's the whole reason the war in the early 2000's started. Nuclear weapons won't be going anywhere as a lot of countries have them and will continue to try and obtain them illegally.
Unfortunately, I do not think that a world without nuclear weapons is possible. First, because of their radioactive nature, there is no sure way to destroy a nuclear weapon that is environmentally safe. Second, numerous smaller nuclear weapons from the former Soviet Union are unaccounted for and may be held by governments or private organizations in secret. Third, because of human nature, conflict is inevitable and the need to develop destructive weaponry for offence and defense is the result of this bellicosity.
I personally feel that a world without nuclear weapons is a pipe dream. Unfortunately, nuclear technology continues to be used for a multitude of purposes, including weaponry. With more countries gaining ground with nuclear programs, such as Iran, it makes it incredibly difficult for nations which have possessed nuclear weapons for years to convince other countries that they shouldn't proceed with their nuclear programs.