Yes they are already on the road, at least in the testing stages. So far they seem to be proving to be safe. I have only read of one accident. The "driverless" car was rear ended and not at fault. Because of the video and data recording systems on the vehicle they were able to get a great eyewitness so to speak.
At this point being "driverless" does not mean no human involvement. A human is still required to be behind the wheel and able to take over if necessary.
While, like some others, I have my apprehensions the technology itself is pretty impressive. If you think about it we are already seeing some of it in new cars. For instance the accident avoidance systems utilizes some of this technology. As time goes on I expect they will introduce more and more. Over time the cars will evolve to the point of being "driverless".
As far as concerns that the car's computer system can fail. As already pointed out the cars being tested have quite a bit of redundancy. That's not to say that glitches can't or won't happen. If you think about it though we face the same issue with human drivers. A stroke or heart attack for instance can easily and does disable drivers and cause accidents. It has also been pointed out that humans tend to become very distracted. Between the phone conversations, texting, eating, putting on make up, etc. it is amazing that some people ever get to their destinations unharmed.
While a little far fetched at the moment I tend to be a little more concerned about the security aspect. Minor programming changes uploaded to these cars could cause some major damage.
I know for some of us all of this is hard to accept. If you think about it though much of yesterday's science fiction is now the norm. Likewise today's science fiction will become the norm in the future and the future is not always that far off.