It appears Uber may be having a small effect on the number of people who want to own cars. This article also says they are working on self-driving cars.
In a recent survey of 2,000 adults ages 18 to 64 conducted by Frank N. Magid Associates, 18% of respondents said they had used Uber in the past year, and of those people, 22% said they are likely to hold off on buying a new car because of the availability of the service.