If you have a harassing neighbour, chances are your home life is stressful right now. It could be as simple as a catty woman across the street who bad mouths you to the other people in the neighbourhood. It could, however, go deeper than that, and you might be dealing with a neighbour who seems to truly be out to harm you. Either way, you have several options for dealing with this type of situation.
Determine who, exactly, is the problem. If you've heard through the grapevine that a neighbour has been bad mouthing you, this doesn't necessarily mean that it's true. You could also be placing the blame on the wrong person. Before you try to rectify the situation, make sure you've identified the problem.
Remain civil. It can be hard to argue with someone who's friendly and lighthearted. You can still be neighbourly by saying "Hello" and smiling warmly whenever you see your neighbour. Even if you don't get on the good side of your harasser, your other neighbours might realise that you're not the problem.
Keep a notebook with the dates, times and details of the harassment. If you end up having to take your neighbour to court, you'll have a documented account of everything that's happened between you. If you've had to visit a doctor to deal with your stress levels, keep the records of that visit.
Use a voice recorder when you're near your harassing neighbour. You may catch the neighbour talking about you to somebody else, or the neighbour may say something directly to you. Either way, having it recorded will give you the proof you need should you have to report an incident to the police.
Call the police if you feel that you or your family could be in danger. While you may want to take care of the situation yourself, your best bet, in order to protect yourself and everyone around you, would be to let professionals get involved. You don't want to take any chances when it comes to your safety. However, don't call the authorities for several smaller incidents that don't present harm.
While having a harassing neighbour is stressful and annoying, remember that it most likely won't go on forever. If the harassment is small and not harmful, you don't have to react every time something happens. Sometimes ignoring bad behaviour will eliminate it, eventually.