Self driving cars will become extremely popular if they prove to be effective. The trouble with automated driving cars is still other drivers. Human drivers will impair automated driving. When interchanging human and automated artificial intelligence, this creates a dangerous environment. Humans are unpredictable in action, thus those that interact with them must be prepared to react to unexpected actions. Finding an AI that can react to the unexpected would make self-driving cars more marketable, whether that input be man-made or even nature-made.
Not only would it become popular, but it would eventually become standard as older models were phased out. There would be a lot of benefits to this. Sleepy drivers could safely nap on their way to work, and people would never have to worry about drunk driving again in their lives.
I think that if a self-driving car existed it would be really popular. A self-driving car is something that a lot of people would find beneficial. A lot of people commute long hours in the day. If there was a self-driving car, people can use while they go to work or go home from their jobs.
The reason that a self driving car will not become popular is because of all the baggage the self driving car brings with it. Self driving cars imply self driving semi trucks, self driving farm equipment, mining equipment, taxis, etc. The general push towards automation, according to a 2013 Oxford study, is threatening 47% of US jobs. The effect this will have is the displacement of large numbers of people who will not be able to afford these self driving machines. If they are to become popular, it will be with a minority of the wealthy, before this decadent civilization hits the wall.
I do not believe a self-driving car would be instantaneously popular. I think many people would avoid such technology until the problems were ironed out, so to speak. I personally like driving, so I don't want my car to do it for me. As a consumer, my ultimate concern would be safety.