It depends on your milage. I already do not awn a car and use car sharing http://www.cambio.be/ They say that if you drive less than 15.000KM (+-10.000 miles) it would become financially interesting. Obviously the more people, the cheaper it will get.
I do not need a car, because I use public transport to and from work paid for by my employer.
1) It is not 'your car', so no bragging about your car
2) You need to plan ahead and pick up your car.
3) You need to be close to a pick up point.
1) Cheaper (if you run less than 15.000KM)
2) No worry about maintenance
3) Take the car you need. Small to large is available.
With self driving cars, the disadvantage 3 will become much less closer. That means more people will be able to use it and that will bring down everything. It this moment I would say you need to drive less than 10.000, because above that, even if cheaper, the advantage of having your car in front of your house or apartment is greater than the money you make. (Obviously YMMV)
That said, it will reduce the amount of parked cars, not the amount of driving cars on the road, because people will still move around the same amount, but added to that you need to add the empty trips to pick up somebody.
Once all cars are automated, it will become more efficient.
Cars will also do more miles per year, but with lesser amount of cars. So in the beginning thgis means fewer cars, but they need to be replaces earlier due to more usage. This would mean that higher quality cars need to be made, because replace cheap cars every year will become very expensive.
I think it will be about 5-10 years to see this happen as many people still want to own a car and like to drive.