Here in the Netherlands it's not at all unusual for a household not to include a car. Lots of adults don't have driving licenses.
These things are all relative, of course, and mostly I make my comparisons to the UK where I lived for most of my life. The UK also has quite a lot of households without cars. The figures for car ownership and affordability compared between the UK and the Netherlands make for interesting reading.
Right up through the 1980s and early 1990s, The Netherlands had slightly higher car ownership than the UK, which was to be expected as cars were more easily affordable in The Netherlands than in the UK. However, in 1995 something changed. Car ownership here in the Netherlands stopped growing while it continued in the UK, surpassing the Dutch rate of ownership.
The 1997 figure for car ownership in The Netherlands showed a slight reverse, with 372 per thousand compared with 373 in 1992.
In 1994 in the UK, 30% of households were car free, and 11% were judged to be unable to afford a car. However, in The Netherlands, these figures were 42% and 7%, giving the widest gap between affordability and ownership amongst the EU15 in the table.
The figures together indicate one thing. More Dutch people make a deliberate choice not to own a car than citizens of other countries in this survey. It's not that they can't afford to own a car, but that they have less of a need of it.
By catering well for people who choose not to have a car, and creating an environment in which cycling is a very pleasant and efficient way of travelling, combined with good transport mode integration, an environment has been created where being car free is a more viable choice, both for families and individuals.
However, you don't have to read far into this data to see that the car is still very popular in the Netherlands. Dutch people like driving, and they like cars. Cars remain more affordable in the Netherlands than in the UK. However, Dutch people are not enslaved by cars. They have a choice of transport modes which work well, and the main alternative choice is the bicycle.
Note that Dutch car ownership figures have risen considerably since the statistics used above were published. By 2010, the Dutch owned 528 cars per thousand people while the British owned 519. Wikipedia has a list of countries by car ownership rate. However while the Dutch have seemingly decided that they like to own more cars than they used to, they're still opting not to use them so much as people of other European nations.