The answer is so different for different people that the question is almost meaningless. I have twin three-year-olds and no car. In NYC, that means we can get anyplace where the subway station has an elevator, can't get anywhere if there's no elevator, and can't go anywhere that isn't along a subway line unless we rent a car.
For many people with children, yes, a car is an absolute necessity.
But more to the point, keep in mind that the answer "I need a car because I have kids" tactfully ends unwelcome conversations with bicycle-enthusiastic non-parents. I realize this will offend a few people, but if you're not a parent, your opinions about parenting are pretty much noise.