It's not essential, as others have said it depends on your lifestyle and where you live.
I don't drive and don't intend to ever learn, I'm a single parent of a 6 year old.
I live in a town in between 2 cities with great public transport.
Pretty much everything we need day to day is within a 30 minute walking distance - DS's school (currently in primary but there are 2 secondary schools in walking distance for when that time comes), my job, 3 major supermarkets and other shops, the doctor's surgery, the dentist, the after school activities DS does.
For things further out we live a 10 minute walk from a bus stop with regular services between the cities, and a 10 minute walk from the train station.
I never get this whole "ferrying teens around" that goes on on MN either. When I was a teen I was never ferried around by my mum who did drive - I was given bus money and made my own way around! We have never lived rurally though so public transport is always available.