With regards to artificial intelligence taking over the world as per Terminator, it seems unlikely at most.  There's a big distincion between a program that doesn't perform as intended and a sentient, willful, technological intelligence.  The prior is quite common, but technology produced for defense contracts tend to be thoroughly scrutinized for quality control, at least in the U.S.  The latter seems close to impossible, especially as an accident.  Intelligence alone produces neither an understanding of the world nor goals to work towards.

I consider it much more likely that technology would be used to allow humans to break the performance limitations imposed by a gradual process of evolution as per Ghost in the Shell or Gattaca.  Whether or not this is a good thing is an entirely different question, but one that might be best answered with "good according to whom?"

Before the "singularity" can happen we need a breakthrough in technology.

All of our current Technology really breaks down to one single component.

The transistor.

We've been using the transistor for over 60 years.  The one real thing that has changed has been the size and number of the transistors in our technology.

We are closely reaching the limits to the transistor capability.

We need to come up with the next thing like the transistor replacing the vacuum tube.

First off, I dislike the term "technological singularity". I have studied both computers and physics my entire life. As for a professional job I took the computer route, although physics has been my second favorite field of study. I have read about this quite a bit, but the terminology has never made sense to me. I do not see how any definition of the word "singularity" fits into this concept, so maybe it was just a cool catch phrase someone picked.

Terminology aside, I have had a similar belief for a long time. At some point, technology will overcome human abilities. We are already witnessing our physical abilities being taken over by mechanical means. You could view this in two ways. One being that we use cars instead of running, and we use guns (or even nukes) instead of choking people to death. These examples demonstrate technological progress taking over our physical abilities. If you deny that as an example, a second example is how the olympics recently denied a double amputee because his bionic legs gave him an unfair advantage (even 30% over able bodied people). I don't think anyone is really disputing that we will be physically beat by mechanical means.

For technology to overcome people in a mental aspect is a whole different story. I would say that deep blue beating the best human being at chess is not a good example of this because the computer is not actually thinking, but it is following a known algorithm for the best moves (even if it was learning to play, that learning process would be a pre-programmed method specific to chess). For real progress in artificial intelligence, we will need to develop a new method of storing and processing data (as watcher pointed out). I think this will come in the form of integrating computers and living things together. There are other possibilities and many companies are doing research into many interesting data processing/storage techniques, such as holographic storage, memory based on electron spin, and even quantum computers.

There has been some great progress in integrating electronics with living things, including the human brain. If anyone is not aware of this progress I strongly suggest researching it more (see links). If this progress continues, we would reach this "technological singularity" with a cyborg species, if not a completely independent computer, or perhaps the cyborgs could create the intelligent computer.

Here's somewhere to start the research:

brain computer interface:

http://en.wikipedia.org/wiki/Brain-computer_interface

remote controlled humans (some reports include video):

http://www.foxnews.com/story/0,2933,173500,00.html

microsoft mind reading patent:

http://www.newscientist.com/blog/invention/2007/10/microsoft-mind-reading.html

sony brain sensation control patent:

http://www.newscientist.com/article.ns?id=mg18624944.600

If you consider any of these sources unreliable, double and triple verify them with google searches. I personally don't trust anything from any single source, no matter how reputable it is.

A fine idea.  I've watched some of Ray Kurzweil's lectures on youtube before.  Im about halfway through one of his books titled "The Singularity is Near".  I love this man he is my hero.  It is very fascinating when he speaks of exponential growth of technology but evolution as well.  He predicts that we will merge with machines.   When he says merge i think he means nanomachines will prevent us from dying(if we desire it, or as he says "Death is a tragedy" , disease, enhance our minds and bodies.  He also talks about the idea of reverse engineering the human brain with either nanomachines or a brain scanning method.  Nanomachines will enable vastly more powerful computers to be constructed and enable human mind simulation.  The idea of nanomachines is very fascinating and something I myself would love to get into maybe in graduate studies.  I've come to understand its vast potential good in the world.  Cheaper products, dirt cheap health care, end famine, and many other things.  He also talks about modeling the human mind to see what all areas do specifically to create strong ai.  As far as timeframe I think it may discuss that in another one of his books. Live long enough to live forever or something like that.  I've been meaning to buy it because I think it discusses ways to be healthy through your diet.  I think he projects at the current rate of exponential growth of certain technologies to be about 50 years for either increased longevity or immortality i cant remember exactly.   

I don't think this is true. We do not have a clear grasp of what true intelligence is (a few hundred years ago, being able to do maths quickly would have demonstrated intelligence what people call intelligence). Also, most AI techniques used right now are treated as black boxes, and cannot easily be checked for flaws - neural networks and genetic algorithms are two common examples. Once we create an AI whose intelligence surpasses our own, I doubt we will have any control over the way it thinks or the conclusions it comes to. It will be too complex for us to understand except on a very high level.

Having said that, I don't think a Terminator situation will happen either, unless we deliberately design computers that are self-interested and dominance-oriented. While we won't be able to control computers' thoughts and actions, we will at least be able to control their high level behaviour, like our own emotions and instincts control us. 

As for the technological singularity, I think it's useless making predictions (If we treat the singularity as a point where computers can make better versions of themselves). AI researchers have been wrong time and time again about how easy/hard things are to do, simply because we don't understand the problem of intelligence well enough.

There have been some interesting developments over the past few decades, but all of our AI research really boils down to some simple, but clever, mathematical/logical techniques that give some semblence of limited intelligence in certain areas. If we really want intelligence in the human sense, we really should be looking to neuroscience, rather than the current techniques of AI, to solve the problem.

 On the other hand, the most promising AI research I've read about so far for capturing human intelligence is described here: http://en.wikipedia.org/wiki/Open_Mind_Common_Sense

This approach seems flawed to me, but it is still a better approach to human intelligence than any other current technology.