IEEE Spectrum has a special report about the Singularity, that point in our future where predictions fall apart because major technical changes make any extrapolation we may make based on today's trends essentially obsolete. Even the New-York Times has an article, entitled The Future Is Now? Pretty Soon, at Least, which quickly brushes up some of the ideas.
The special issue in IEEE is more extensive. There are many interesting articles. In one of them, Ray Kurzweil, arguably the inventor of the concept of Singularity, debates with Neil Gershenfeld, and Vernor Vinge shares what he sees as the signs of the Singularity.
One important point, I believe, is that "there will be a singularity at time t" is a proposition that might depend on the time it's being enunciated. It seems very likely to me that when you are in the middle of a singularity, you have no idea that it's there. That's why I am a bit wary of the use of a singular noun, the singularity, when I think really that there have been many singularities over the course of history.
How could someone from the middle-age, for example, predict the structure of a society after motorized personal transportation became not only possible, but mainstream and relatively cheap (I know, I know, gas prices...)? In other words, seen from the middle-age, the invention of the automobile or, even more so, the airplane, were singularities that might be predicted (e.g. by Leonardo da Vinci), but whose impact on society was really difficult to grasp. The same is true for remote communication, from the telephone to television to the Internet.
Now, one singularity is somewhat special, and it's when we started building enhancements to our intelligence, and not just our physical abilities. That's the very definition Vernor Vinge uses when he writes:
I think it's likely that with technology we can in the fairly near future create or become creatures of more than human intelligence. Such a technological singularity would revolutionize our world, ushering in a posthuman epoch.But that already happened. The first modest pocket calculators enabled computations so complex that they completely changed the course of engineering. Any engineer with a calculator has "more than human intelligence", for he can compute faster than any human being without a calculator can. It's only recently that we redefined intelligence to exclude the ability to perform computations, and the only reason we did that is because computers were so much better at it than we are.
So that's my personal view on that question: the most important singularity, the one that Ray Kurzweil sees sometime in the future, has already happened, and we are right in the middle of seeing its effects.