I think self driving cars and public transportation could ultimately have a symbiotic relationship. If self driving cars result in significantly decreased car ownership, there will be plenty of traditional car trips replaced by the self driving variety, but there will also also be traditional car trips replaced by public transportation.

If I live 20 minutes outside the city, but not within close walking distance to a transit stop, I am currently forced to drive to my destination, even if it is located somewhere along the public transportation network. With a self driving car, I could be taken to the closest transit stop, and then ride the subway to my destination to avoid congestion.