Without a car, everything transportation related has to be planned and weighed.
I moved to Tokyo 5 years ago. If I want to get somewhere, I walk to one of three train stations within a 10 minute walk, hop on the train, and am there in – usually – about 30 minutes. There's always the option to take a taxi, but they're often no faster than train. I can still drive out to the mountains if there's no train to the one I want to climb, because there are more car rental shops within walking distance than there are train stations.
Sure, there are cars in this city. They're useful tools that make a lot of sense for many people to own. But the average person chooses to live without one, because in a city designed for people instead of cars, life can actually be better that way.
With that said, more power to those people that don't want or need one, life is all about what works for the individual.