I don't want to be a party pooper but I am kinda worried that self-driving cars are an ecological disaster in the making. We already need to limit GHG emissions, and switching to public transport is a good way to do it. However, with self-driving cars, one of the main incentives for public transport (you don't have to drive) is gone.
Presumably once you have full autonomy in some number of decades, you'll also have a lot more electric vehicles and renewables. That said, there's every reason to think that you will see vastly more miles driven. What may encourage transit is the increase in miles may make cars in urban cores that much less tenable.
Self-driving cars are going to bring the cost of a trip way down and when the cost of something drops, we tend to use more of it. Rather than a big shared fleet, I suspect people will continue to buy their own cars and will in fact own more of them because (eventually) they will be much less expensive than current vehicles.
People already spend far more on their cars than they really have to and I doubt that will change.
On the plus side, I think the inexpensive cars of the near future will probably be small and electric with a much smaller operational carbon footprint. On the down side, when you have a robot chauffeur, the value of proximity drops and so I think they will fuel sprawl like nothing else before.
I guess I'm saying I have no idea what's going to happen, but I doubt it will fulfill the Polyanna prophesies that I sometimes read about.