Cars will, one day, drive themselves.
The technology is not an issue. Between the DARPA Grand and Urban Challenges, the ability of an automobile to get about safely on its own will surpass that of a human driver in the next few years. Actually, relative to some drivers I've known, robotic cars are already far better. Add another five to ten years beyond that to make the technology cheap (less than $1,000 per vehicle) and autonomous automobiles will be ready to roll by 2020 (more or less).
But will cars drive themselves by 2020? Some might, but I doubt that very many will. There are many cultural issues that will stymie the adoption of robotic vehicles.
The biggest problem is that even a car that has perfect software will still occasionally get in an accident. Its frequency of accidents will be far below that of an average human, but it will still get in accidents. Driving on roads is sheer chaos. Sensors will stop working, joggers will jump in front of the cars, bicyclists will bound on by, meters will malfunction, streets will be unexpectedly slippery, etc. It's not clear how blame for accidents involving robotic cars will be assigned and how the damage will be paid for (I've given one humorous example here). My observations lead me to believe it will be many decades, perhaps even centuries before these critical issues are resolved. If every time someone is killed in an autonomous automobile accident (and it will happen), the software company is bankrupted via lawsuits, robotic vehicles will never gain any traction. That would be true even if they reduced automobile accidents by a factor of ten overall.
Ultimately, I think demand for such vehicles will be so strong that we'll figure out the legal and cultural aspects. The military will drive the technology whether or not there ever are non-military robotic cars. After all, the military uses far more dangerous weapons and people are killed all the time. For the military, safer and higher performance are better, even if people still die.
The elderly will increasingly need cars that drive themselves. Many states are now taking away licenses of older drivers who are likely to be high risk (for example, because they can't see). But taking away licenses has a huge cost of its own. It consigns the elderly to their houses, making it very difficult for them to get out and receive the stimulation required to maintain physical and mental health. It also makes it difficult for them to get groceries, buy clothes, and otherwise take care of themselves, leading to earlier transfer of these citizens into expensive assisted living situations.
For the elderly, cars that can drive themselves are the perfect solution. They needn't endanger themselves and others, yet they still would have the mobility they need. In fact, their mobility will likely increase, since many elderly drivers avoid going out at night because of vision issues.
So that's where I see robotic cars getting their toehold for non-military applications. The clout of the elderly voting bloc (and their children) will force the legislation required to enable the elderly to have such vehicles. I'm hoping by the time I'm old enough to need a car to drive me (approximately 2040), that we'll have gotten through all of the necessary societal hurdles.
Once this happens, I predict the flood gates will open. Taxis will drive themselves, greatly reducing cab fares. In fact, I predict that cab fares will be so greatly reduced that more and more people will take taxis everywhere and won't even bother owning a car. The autonomous taxis will be so smart that there will always be one of just the right size available for you and the group you're with right when and where you need it. Eventually, almost nobody will own a car since having a car sit in your garage is allowing a great deal of capital equipment sit idle.
Cars will talk to each other (electronically). As a result, they'll be able to drive much closer to each other which will enable far more of them to fit on existing roads even while traveling at much higher speeds. Most cars will have one or two seats enabling even more cars to fit on the roads. Fuel efficiency will increase further since the cars will "draft" off of each other. It will be possible to fit approximately 5 times as many cars on a typical freeway.
I see all of this happening within twenty years of when cars begin driving the elderly about. The first step is the hardest, the rest will happen very quickly.