The city of Vienna did this with their major shopping artery (Mariahilfer Straße), despite an enormous amount of skepticsm. They closed off all traffic in some parts, and most of all traffic in others (to allow for crucial intersections). Where allowed, traffic is limited to a pedestrian tempo.

The experiment was a huge success. Commerce has never been busier. I don't think that the drivers miss the roads, and the biggest skeptics -- the shopowners! -- are the greatest benefactors now.

They're extending this concept to further areas now. Promote pedestrian, bike, and public transportation traffic, reduce or eliminate everything else. It's great.