In 1945, one nation had nuclear weapons. By 1949, there were two. 1964, five. Today, probably nine.
By now, any industrial nation could develop fission weapons if not actively prevented. Any advanced nation could probably develop fusion weapons.
A matter of a decade or two, it will be possible for half the countries on Earth to make nuclear weapons. A while ago, I suggested that one day a kitchen device would be able to synthesize arbitrary chemicals; if nanotechnology fulfils its promise, then uranium enrichment could become a garage activity. Twenty-five years? Fifty? I can't see it taking a hundred.
Since 1945, various strategies have been put forward to protect against nuclear attack.
One of the first suggested was world conquest. Robert Heinlein was very insistent in the 40s that the only sane course was for the USA to conquer the entire world before any potential enemy could develop nuclear weapons.
Disarmament was another widely recommended option - stuffing the genie back into the bottle.
The two strategies that were actually pursued were deterrence and non-proliferation. Deterrence worked - and innovations such as submarine-launched missiles reduced the first-strike threat. But as the number of nuclear powers increases, the reliability of deterrence falls, as the possibility of a concealed or deniable attack increase, and there is more chance of a foreign power being desperate or crazy enough to not care about deterrence.
Non-proliferation may have slowed down the spread of nuclear weapon technology, but in the long run, it is failing.
So how bad is the long-run outlook? It is seriously worrying. If, in 2060, the likes of Mohammed Siddique Khan and his associates (or Timothy McVeigh, or David Copeland) can produce a few atomic bombs in a house, it seems inevitable that sooner or later we would see a level of destructive nuclear terrorism which could totally destabilize our society - in the way that present-day terrorism - with home-made bombs, sabotage, and assasination - simply can't.
What about the nearer future? Say 2025 - enriched uranium is still outside the reach of the hobbyist, but there are 100 or 200 potential or actual nuclear powers in the world. Some of them are politically unstable. Some of them are our enemies. How long can such a situation endure without a society-destroying state or state-sponsored-terrorist nuclear attack?
It's very difficult to say.
Somehow, I'm just not too worried by all this. It's just too hard to predict politics that far into the future with any confidence. You can pick one issue - nuclear proliferation - and project and speculate as to how it will develop, which is what I've done. What you can't do is take all the other areas which might change the environment, and predict how all of them will develop over decades. What countermeasures might be developed? How will the world economy change? How powerful will satellite surveillance become? What totally unexpected technological, political or economic development will change the game beyond recognition?
That's not a conclusive reason for letting the future fend for itself. I'm trying to draw a distinction between the forseeable consequences of our actions, which we must evaluate and include in our calculations, and the attempt to predict and manipulate the state of the world in the far future, which is hubris. Projects which will bring long-term benefits are certainly worthy of consideration, whether they be irrigating the deserts, or developing new energy sources, or anything else useful - we are not sure how valuable their results will be, but if, appropriately discounted, our best estimate is that they will pay for their costs, then they are worth doing. But projects whose value depends on particular assumptions as to the state of the world in the far future - that we will be allied to certain types of government, or that the balance of state versus individual power will move in a certain way - well, given the right assumptions almost any policy can be justified, including policies of "bringing forward" future and actually quite unlikely conflicts to the present.
Update: A more alarming assesment of the current nuclear threat from the Bulletin of the Atomic Scientists