Big caveat... my experience may have been affected by the time of year I visited (mid-April). Perhaps conditions are better during peak summer visiting months. But to start... I ran into several problems with the system. First of all, the bikes were few and far between to be found throughout the city. Second, more than half of them that I did track down had a defect with the locking and unlocking mechanism. Third, about 3/4 of those I could unlock were unusable due to various mechanical defects. Finally, the city maps on the bikes that show the locations of the racks are probably out of date. I could not find more than a few of the racks in some of the indicated locations. Copenhagen really is one of the world's great cities for cycling, and even though it was hard finding a usable City Bike, when I finally stumbled upon one, it really improved site-seeing efficiancy. But if I return, I will probably pay to rent a bicycle from a commercial agency.
We'll be heading to Copenhagen in a few weeks - thanks for the tip, Tom! If we bike, we'll make sure to rent from a commercial agency!
One unexpected glitch with the Copenhagen City Bikes was that all the ones we found seemed best suited for people medium-to-tall heights who could manage clunky male (bar in middle) bikes in moderate traffic. If you are shorter or uncertain on clunky bikes, don't bother because these bikes could be hazardous for you to handle.