The Internet has opened up the world to many. Like life in the real world, if you open the door too wide in the cyber world it is likely some vermin will creep in. By now most have heard of the Megan Meier/ MySpace case, where a teenager committed suicide after being "cyber bullied" by the mother of a former friend. You can (due to the marvel of the Internet) read about it by searching a few words. The mother was prosecuted and many states have considered initiating legislation to prohibit Internet harassment. There is also, especially in these economic times, a lot of unlawful activity with phoney emails posing as your bank, your internet provider or other service provider where the bad guys are actually trying to obtain your personal financial information to defraud you or a business using such information. "Identity theft" being facilitated by fraudulent means via the trusty and easily accessible web. Stalking, once typified by personal and unwanted visits, phone calls and other contact, can now be accomplished by setting up "front" email or instant message accounts and has now been elevated to an instantaneous and dubious frequency in the cyber world.
Realize first that individuals who resort to such sick and anti-social behavior have problems. They cannot handle issues in an adult fashion and often have to hide behind pseudo identities. Depending on the jurisdiction you live in, you may be able to avail yourself of both civil and criminal remedies against the perpetrator. Civil remedies are those you can pursue through the Courts, either in "propria persona" (representing yourself) or with a lawyer. Depending on what you are seeking, you may go to Small Claims Courts (where there are often advisors available to help you) or through the higher Courts. The activity may also constitute a crime, which can be pursued by the police and prosecuted by the District attorney. There are also agencies which can guide you including the Federal Trade Commission, Postal Inspector or the Internet Crime Complaint Center. A very useful link is: http://www.lookstoogoodtobetrue.com/complaint.aspx
As above, what constitutes a crime may vary from state to state. However the Internet is an "interstate" mode of communication and may constitute a Federal offense. I presume the law will continue to evolve with the advancement of technology and legislation will continue to be proposed to keep up with the latest trends. As to civil causes of action, in California for example, the barrage of unlawful cyber "attention" may constitute Defamation, Invasion of Privacy, Infliction of Emotional Distress, Interference with Contracts of Economic Advantage and more. The "bully" may seek to injure you, your business or just your peace of mind.
The Internet is not a license for cowards and law breakers to hide behind a cyber mask. If you have been victimized, use the Internet as a sword as well as a shield. A little bit of browsing, including the link I provided above, will tell you that you do not have to put up with such nonsense and unlawful behavior. Search out what is available in your locale, including the police, the courts and administrative agencies. The cyber "information highway" can lead you to an answer to your problem. Rest assured, the highway is being patrolled for law breakers and you can do your part by reporting and cooperating with the authorities to bring the violators to justice.