A weapon of mass destruction (WMD) is generally taken to be a type of weapon which is designed to kill large numbers of people, usually civilians but also potentially military personnel. Weapons of mass destruction are generally considered to be of limited military usefulness because their destructiveness is likely to trigger an extreme response.
formerly known as "NBC weapons"
The types of weapons traditionally considered to be of this variety are:
The abbreviation "NBC" was used to refer to these. However, new technologies such as genetics, proteomics, molecular engineering, artificial intelligence and robotics, led to new concerns that are hard to qualify since these technologies have not yet been (and hopefully will never be) used in war.
One concern was that the different treaties applicable to each of the "NBC" trio had legal loopholes, due to confusion about the line between chemical and biological weapons (e.g. prions which are not organisms but simple single-molecule proteins, and could thereby be considered either chemical or biological), and the spread of "dual use" technology through commercial channels that could easily be put to military use.
now includes genetic, proteomic, robotic and AI threats
Another concern was that most "NBC" treaties predated the ability to DNA-sequence and genetically modify biological entities (to be, make or carry poisonous substances, virus or prion), e.g. altering the well-understood e. coli bacterium to generate anthrax prions, which is considered to be technically feasible, and hard to detect.
The early treaties also did not anticipate nanotechnological molecular engineering methods to generate new molecules with lifelike characteristics, or to exude substances useful in chemical weapons.
Nor, finally, did it anticipate the danger of efficient and miniature weapons-grade robotics to control all of the above, nor artificial intelligence and computer graphics to train, brainwash, motivate and guide human carriers of such weapons to their targets. Modern video game technology indeed may be sufficient to train such terrorists or suicide bombing kamikazes, including evasion of detection by guards.
For these reasons, the more generic phrase "weapons of mass destruction" came into use, and is now generally used by international institutions, e.g. UN Security Council, in assessing and describing threats. Lack of clear treaties has enabled arguments, especially in the United States, that there is a duty to strike first and disable any state or entity deemed to be developing such weapons. Except, of course, itself.
beyond human control?
Some of these technologies could have impacts far beyond a single generation of the human species in one place on Earth, and so are generally considered to be wholly inappropriate for conflict between nation-states. The only use of such weapons seems to be threatening human extinction (as North Korea began to do starting early in 2003) or mutual assured destruction of an opponent who attacks first - perhaps including other populations innocent in the conflict.
Miniaturization, mastery of genomes and proteomes, and adaptive software, all seem to have the potential to be combined to create pseudo-life-forms that may compete successfully with natural life. Indeed, some scientists in the artificial life field believe it is desirable to do so. The dangers of these technologies in combination, and of loss of human control over biological or robotic runaways, is a major reason that the United Nations seek to control their spread, especially to non-state actors such as terrorist groups, that typically have no population to defend, and so can be quite reckless, and are not concerned with the threat of retaliation against a nation.
Countries that may possess WMD
According to the Federation of American Scientists, over 30 countries may possess WMD by the most common definitions. Their assessment is at http://www.fas.org/irp/threat/wmd_state.htm