Facebook is the world's biggest social networking site today, and has many millions of members from every part of the world. It's very easy to have many friends that you can acquire from numerous sources through out the site. You can agree to add friends to your group from games, personal requests or from searches you do for wither random or specific people. The safest thing you can do is to only accept people you know as friends so that you are likely to have only friendly contact. The problem is when you accept people that aren't close friends or family, people you don't know well. Many games in facebook encourage you to add as many friends as possible to your group so that you gain bonuses like points or game money. This means the games are easier to play and you can enjoy them more, it also means that literally anyone can see details about you from your profile, and in small cases this could lead to abuse.
This very, very rare but does happen in some cases and you need to beware what you can do. Cyber bullying is when a person bullies someone through the Internet and any of its programmes. This therefore includes face book and any of its included programmes. The bullying can come in the form of messages posted on the main boards and on boards linked to games. There are a number of things you can do if this happens to you. One thing is to make it obvious to all your proper friends that this person is a bully that you have added by accident and what they said should be avoided. Next contact the bully to explain what you have done and why, you can go via the settings page to where you can block people from contacting you. This only works though if you know the bully's email address. Otherwise try and block the game you are being bullied from if the attacks are linked to just one game, if linked to more it's harder to block.
You can choose which games you receive emails or updates from so that will block some of the access to you, you can also change your player name in many games so you are harder to follow. You could even decide to take the drastic measure of opening a new facebook account and deleting the one where you are having trouble. This is drastic and time consuming but may be needed, you can aim your true friends to this new place. In another method you could simply ignore messages you don't like or don't appreciate. If just game updates you can block them, if more malicious try the mentioned techniques and consider reporting the problem to facebook. You need to try and save any messages on email, write down and time date any other messages, get all the information possible.