Do Identical Twins Have Identical DNA?

It has long been thought that identical twins must have identical DNA, since they came from the same fertilized egg. The usual explanation for any observed differences between identical twins was that they were caused by environmental factors such as diet, exercise, or exposure to chemicals.

Now we know that the DNA of identical twins is not always identical. That's because as cells divide over and over again during normal human growth and development, some sections of the DNA are omitted accidentally once in awhile. Other sections of the DNA are duplicated unnecessarily. The result is that some somatic cells and even tissues and whole organs may have one to three copies of some genes, instead of the usual two. Such copy number variations occur rarely in all people, not just in identical twins.

It would be helpful to know whether copy number variations contribute to specific human diseases, and (out of curiosity) whether copy number variations contribute to the slightly different phenotypes of some "identical" twins.