For all you fans of game theory out there, here is an argument for why only the US should have nuclear weapons.
Assume that very stable democracies want to stay stable democracies. Also, assume that one of our important goals is to avoid having anyone use nuclear weapons.
Weapons of mass destruction are hard to make. This is actually an empirical fact, but for an argument, if they were easy to make then we never would have evolved as far as we have as a species.
To make WMD you need a large number of people to cooperate in many and varied ways. We need universities and large amounts of funding, and people who are able and willing to work together for long periods of time under conditions of various governments and economic, social and political conditions. From all the cooperation literature we know that cooperation generally implies a peaceful socitey. A peaceful society, if it is a democracy, wants to stay that way. So it will not use WMD if it can avoid it, on pain of loosing their peaceful status.
Non cooperative countries, that is, countries that have not developed sufficient internal cooperation to build WMD have less need to stay stable, because they are not stable to begin with. Moreover, non-democracies have less insentive to avoid using WMD because they are not all that interested in not killing their citizens, because their power does not derive from the people whose lives are in danger. That is the nature of non-democracies. So getting in to nuclear conflict is not the big destabilizing factor that it would be in a stable democracy.
So the upshot is that coutries that 1) are stable democracies and 2) developed the resources and technology on their own, and did not purchase it from others should be the only ones with nuclear weapons. Of course it is preferable that that non have it. However, as long as there are other countries and this is the most effecient way to maintain the stability then it it moral. Moreover, for the same reasons, it is imperative that those countries who are morally justified in having WMD, ought to prevent those who are not morally justified from having it.