Interesting to see comments about bike commuting in Stockholm and London since I tried it in both cities. Commuting by bike in Stockholm is a breeze even if you are biking in parts of the city with lots of traffic. Its also a beautiful city which adds to the experience.
I have tried to commute by bike in London but its to scary for me. I think it would be fine if you can find a path through residential areas, but for me thats impossible. Biking in the central parts of London I feel that a slight lapse in concentration could end up with a very bad accident.