I like the idea of a self driving car because I might not need to use cabs anymore after drinks or in a foreign city. I assume the next step in self driving cars is a hive mind to keep "safe" as many people as possible. One car in accident, ping other cars to take alternate routes, slow down/go around etc. Hive mind would also be great for cars to have fast lanes that just go insanely fast and cars entering and exiting with little fear of accidents (ie: Lane change at fast speeds within inches of each other without being considered "cutting off" someone).
Now, for me, self driving cars would also make me wonder whether ownership of cars is even necessary anymore. Buy a membership/lease and grab a car or request a car type (pod vs multi pod vs transport size) and it drives to your place or to meet you. Kinda similar to car to go or a car rental company or something in between. Heck think of the parking space saved since you don't need gaps in between cars to open doors. OMG think of all the valets that lose their jobs! EVIL!
But then again, imagine going to work and the car drives itself to the mechanic/is replaced by a no problem car? OMG think of all the exercise lost since we won't have to walk as far to cars!
I would expect to see self "driving" in commercial vehicles first. Especially trains on tracks. After that transit, semis and then perhaps commercial level products. I don't think driving will ever completely die out, but perhaps it might not be considered a skill necessary essentially for life survival. Think... a horse. Horses didn't completely disappear after their use for travel was rendered "obsolete". It just became a hobbyist activity. The activity itself didn't just disappear.