A fairly radical new concept in transportation planning emerged a few years ago in the Netherlands, and has rapidly caught on in Europe. It's called "shared space." At its core, this means allowing cars, pedestrians, and bicyclists to share the same space. As Hans Monderman, who pioneered the concept, explains,"When you don't exactly know who has right of way, you tend to seek eye contact with other road users ... You automatically reduce your speed, you have contact with other people and you take greater care."
You'll get a clearer idea by watching this short video about the City of Auckland, New Zealand's plans for implementing shared space on several streets.
More details about the concept are also available on the Project for Public Spaces' blog. There's also a good article on shared space on Wikipedia, with a number of links. Could something like this work in the U.S., or would it require too big a change in motorists' behavior?