Copenhagen is all about bicycles. I know there are other places in the world where people probably use their bicycle just as much as in Denmark, but I'm not sure they do it the way the Danes do. With style and no matter what the weather.
Bikes are definitely the best, fastest and cheapest way to get around Copenhagen. Forget about cars. They are so ridiculously expensive in Denmark due to high taxes, and very few young people have them.
Usually Copenhageners don't buy a car until they get a family and kids. And if they live in the center of Copenhagen they will probably prefer a cargo bike in order to drive their kids around. Much cheaper and faster than a car and better for the environment.
As a tourist in Copenhagen you really must rent a bike. And remember to try the cute rickshaw services, i.e. taxi bikes. You usually find them on Amagertorv in front of Cafe Norden. Young boys and girls will take you to your destination on their bikes.
I'm going to end this post by linking to Mikael Colville-Andersen's amazing film filled with gorgeous images from Copenhagen and its cyclists. I get homesick every time I see it!