Most traditional computer crimes are breaking into a person's account to spy on what they do, and to gain access to their private accounts usually to steal their money. While this is a problem, but at least it is limited to individuals.
Of late, cyber-criminal have gotten much more savvy and daring. They are now able to break into corporations and steal on a grander level. For instance, just a few week ago, criminals were able to access ATMs in New York, and on a single day stole an obscene amount of money.
However, the most serious crimes are now being committed on a international scale. Recently, President Obama met with the president of China to discuss national security. Such a meeting was important, because nations are steal from nations through computers.