Acording to this Newsday column by Paul A. London:

American medicine is a paradox. This is where you want to be for a heart transplant and where most of the world's cutting-edge medical research is done. But America is also a place where thousands of Americans die each year because doctors forget to recommend shots for flu and pneumonia. These problems and others would be greatly reduced by computerized information systems that are already used at a few advanced hospitals and in some medical practices. The failure to adopt these systems more broadly is the unmistakable symptom of an industry whose culture and organization have not been forced by competition to keep up with modern capabilities, not of a confused payments system.

He makes some good points, although I would have liked to hear specifics about countries where they do it better. I wouldn't be surprised to hear Denmark was one, but I suspect the list isn't huge.