Yes, they do exist.  Here are 7 favorite car-free cities as selected by the Mother Nature Network, which reminds us that a mere 100 years ago just about every city in the world was car-free.  Large to small:

The Medina of Fes-el-Bali, Morocco (bottom image) - pop. 156,000.  One of the largest contiguous car-free urban areas in the world, if not the largest, and the most pedestrian-scaled as well, where cars simply wouldn’t fit on most of the streets, sometimes not even bikes!

Venice, Italy - pop. 70,000.  Venice is host to one of the best collections piazzas in the world - there’s one practically every few blocks, and in warm weather they’re full of people.

Hydra, Saronic Islands, Greece (top image) - pop. 3000.  A popular destination for nearby Athenians, Hydra features horses and donkeys as its main inland transportation, though most everyone walks.

Lamu Island, Kenya, Africa - pop. 2000.  The ‘oldest and best-preserved Swahili settlement in East Africa’, a tourist destination, and reliant on donkeys for transportation.

Mackinac Island, Michigan - pop. 600.  Home to two of the largest freshwater sailing events in the world, with motor vehicles banned since 1898.

Sark Island, United Kingdom - pop. 560.  Award-winning hotels and restaurants, camping on this island in the English Channel. Only horse-drawn vehicles and bicycles allowed. 

La Cumbrecita, Argentina (middle image) - pop. 345.  Reminiscent of Swiss mountain villages, the self-described ‘pedestrian town’ focuses on eco-tourism.

Check out a complete list of car free places on Wikipedia. It makes you wonder why city and business leaders make such a big deal about developing just one pedestrian-oriented street. At least New York City is taking some initiative by closing 36 blocks of street to cars, including Times Square, reversing a trend starting 100 years ago.