Absolutely!!
If the city has a quality, 24x7 mass transit system, why bother with a car?
I grew up in NYC, and never had a car, until I joined the Air Force and got sent to California, where it was impossible to get around without one. For the last 30 plus years I've lived in Nebraska, again, where it is pretty much impossible to exist without a car.
But I also lived in Berlin, Germany, and for four years had no need of a car, and no problems living without one.
I seem to recall a columnist I was following a couple years ago who was based in Philadelphia, who often noted that most of the time he neither needed nor wanted a car. Living in the city center, a car was far more trouble than it was worth. But he also noted that Philly had come up with something (??PhillyCar??) where you subscribed for something like $50 per year, and then you could go to any of over 100 offices around the city and "check out" a car, for as little as a day, or as long as a week (with some fees based on usage longer than the hour). I'm vague on the details now, as I never lived there, but it struck me then that such a system would make great sense. No car to worry about or pay for, for the 95% of the time you didn't require a car, and an easy, inexpensive system to obtain a car for that 5% of time you did need it.