The objectives of bullies are Power, Control, Domination, Subjugation. They get a kick out of seeing you react. It doesn't matter how you react, the fact they've successful provoked a reaction is, to the bully, a sign that their attempt at control have been successful. After that, it's a question of wearing you down. The more your try to explain, negotiate, conciliate, etc the more gratification they obtain from your increasingly desperate attempts to communicate with them. Understand that it is not possible to communicate in a mature adult manner with a disordered individual who's emotionally retarded.
The Number One rule for dealing with this type of behaviour is: don't respond, don't interact and don't engage. This is not as easy to do as it sounds. It's a natural response to want to defend yourself, and to put the person right. However, never argue with a serial bully; it's not a mature adult discussion, but like dealing with a child or immature teenager; whilst the serial bully may be an adult on the outside, on the inside they are like a child who's never grown up - and probably never will. Serial bullies and harassers often have disordered thinking patterns and do not share the same thoughts or values as you.
The second rule is to keep all abusive emails. Create a new folder, perhaps called "Abuse", and move hate mail and flame mail into this folder. You don't have to read it. When the time comes to take action, this folder of hate mail and flame mail is your evidence. Bullies, especially cyberbullies, are obsessive people and if their account is closed down you may start receiving mail from another address. This can later be compared to the abusive emails you've already received to identify the perpetrator. You'll find the same words, phrases and strategies occurring.
The third rule is to understand bullying. Read through Bully OnLine carefully, understand the profile of the serial bully. Recognise that you are not dealing with a person who has the same mindset as yourself. Bullying, and especially cyberbullying, has links with stalking - see www.bullyonline.org/related/stalking.htm for links to stalking sites.
Rule four is get help. If you're a young person, this is essential. Even mature experienced adults often cannot handle bullying and harassment by themselves. Sometimes you are dealing with a severely disordered and dangerous individual.
Rule five is become alert to provocation. It could be called "The Baiting Game". A provocative comment is made and those who respond spontaneously in irritation (eg non-assertively) are then encouraged to engage in conflict with those who respond without irritation (eg assertively). The provoker watches, waits and stirs the pot with the occasional additional provocation. What interests me is the sense of gratification that a provoker gains from watching others indulge in destructive interaction initiated by him- or herself. In this context, gratification is a perverse form of satisfaction akin to, but distinct from, pleasure.
The sixth rule is become an observer. Although you may be the target of the cyberbully's anger, you can train yourself to act as an observer. This takes you out of the firing line and enables you to study the perpetrator and collect evidence. When people use bullying behaviours they project their own weaknesses, failings and shortcomings on to others. In other words, they are telling you about themselves by fabricating an accusation based on something they themselves have done wrong. Whenever you receive a flame mail or hate mail, train yourself to instinctively ask the question, "What is this person revealing about themselves this time?"
The seventh rule is decide if you want to take action, and if so, prepare carefully and strike hard. Sometimes refusing to respond and engage will result in the cyberbully losing interest and going off to find someone easier to torment. Sometimes though, especially if there has been interaction in the past, the cyberbully is so obsessed that s/he cannot and will not let go. You will have to make that person let go, but only through swift, hard, legal action, and only when the time is right. Don't deal with the abuser yourself (this encourages bullies and stalkers), use a third party such as a solicitor.
Finally a reminder - never try to mediate, negotiate, conciliate or otherwise deal with a bully or stalker yourself. Always remember Rule #1: don't respond, don't interact and don't engage.