It's relatively easy for large cities like Rome to become very livable by declaring a car-free zone: population densities are so high that it pays, on many levels, to have a dense public transportation network that operates frequently and inexpensively. On the other end of the spectrum, it is also easy for very small villages to go car-free: nothing is far away, and everything in the village is easily accessible on foot.
Very few small villages have the gumption to declare themselves completely car free: The entire planet is dotted with tiny hamlets literally embracing some throughway (the "Main Street") where cars and trucks tear through on their way from elsewhere to somewhere else, leaving only exhaust in their wake. Even Transition Town Totnes at the edge of Dartmoor, one of the most progressively green small towns, has so far only declared a single car-free day, in September 2012.
In contrast, many small towns in mountainous Switzerland have the advantage that they have always been hard to reach by car, and a few have an additional economic motivation to remain car-free altogether, peace and quiet being part of their brand. The valley of Lauterbrunnen is dotted with small villages that are completely car-free year round, like Mürren, the ski resort where Sir Arnold Lunn laid out the first competitive slalom course.
On the other side of the valley, the town of Wengen has a permanent population of 1300. It is perched on a ledge on the valley wall, 400m above Lauterbrunnen in the valley floor, and nearly 1000m below Männlichen on the nearest ridge above. You can get there by cog train, by cable car, by hiking or by skiing.