Why?
1. Greater safety. Most accidents are caused by human error. Remove the human from behind the wheel and you remove - or at least drastically reduce - human error
2. More free time to do other things. Think of the office workers who have long hour long commutes. That hour long drive behind the wheel could be spent doing something else like - working or power napping or something else, while the car drives itself to your destination.
3. Cheaper and more flexible access to transportation. With self driving cars you don't need to know how to drive to own a car or use one by yourself. In fact, owning a car becomes less of a necessity and more of a luxury. How so? Well taxis would become more available and more affordable because there's no human taxi-driver to be paid. Removing the labor cost involved in public transportation would significantly reduce the cost. The cost of insurance will also drop once it becomes obvious that automated self-driven cars are safer. This too will further reduce cost. And because these cars aren't driven by humans you can have 24-hour access to transportation even in countries that don't have 24-hour working days!
When you combine self-driving cars with improvements in GPS technology, a tourist can go to a foreign country and literally go anywhere at anytime without fear of getting lost! Every location will have a GPS address - even homes, and maybe even mail! No more hassles trying to give a taxi driver confusing or complicated directions on how to get to a person's private home. If someone gives you their GPS address, you don't have to worry about how to get there - the GPS-enabled self-driving car will figure it all out. You don't ever have to worry about getting lost! Think of the freedom of travel that opens up for the tourist!