Cabs in the West are expensive because drivers need to be paid more and cartels are at work. If both these costs are eliminated then what works in a country like India is, suddenly, the best option for commuters in the West. Realtime pooling of cab passengers is a possibility, a traveler could be offered a choice of picking a co-traveler for a reduction in fare(or even cash back!) when already travelling in the car.
Families could still own cars, but they will probably pay for insurance on a per-mile basis, rather than a per-month basis, so that the incremental cost of owning a car is minimal. Effectively, you end up owning a cab that only you use and pay cab fare to the insurance company :-) The ratio of cabs to private cars would then be an interplay of insurance costs/parking costs and ride sharing benefits, with cities leaning towards cabs to escape parking costs. So, things wouldn't be too different :-)
One unfortunate consequence could be the increase in suburban sprawl and traffic congestion with driverless cars as people start caring lesser about longer commute times. Automated cars will probably be better behaved in traffic, but the road capacity will be pushed to its limits.