Groningen, Netherlands.
Since the 70's they have been investing in bicycling infrastructure. I lived there in 1992-1993. A few examples:
1. the downtown area is divided in 4 quadrants. To move from one quadrant to another by car you have to leave downtown and take the ring-highway. This had made the downtown area low traffic (but not low activity). By bike, you can freely move from one quadrant to another.
2. Intersections with traffic lights have special painted areas where bicycles can move in front of the cars. They have their own signal that turns green about 5 seconds before the cars get a green light, so bicycles can navigate safely thru the intersection.

And it does work. 47% of short trips (up to 5 miles) is made by bike in the city of Groningen. That is incredible, even by Dutch standards. In 1993 it was crowned the world's(!) most bike friendly city by Bicycle magazine. Read a review of the city policy here: http://www.context.org/ICLIB/IC39/TruePP.htm

Duppie
(Nowhere did I see this thread limited to US cities. If so, my vote would go to Chicago, my adopted hometown since the mid-nineties)