I don't think we'll remove the want to use cars, nor indeed do I think they'll be gotten rid of, but the notion of private ownership of cars, outside of collecting them as a hobby, is something that will change, if only because the space and resources necessary for them simply won't be there, or will be too expensive for the majority (if we're assuming no change in society - if it goes balls out socialist then i suspect it will be far, far quicker and not driven by oil becoming too expensive.
Don't get me wrong, I absolutely love cars, but as something that billions of individuals own and use they're an environmental and social disaster, from production all the way through to use.