Noise complaints are probably one of the most common issues with neighbours. Most of us are able to tolerate the occasional party knowing that it is not a regular occurrence or the regular weekend lawn mowing knowing that it is a common suburban activity, but when your neighbour decides that they are going to do band practice every Saturday from 3.30 in the afternoon till 10 at night, or 7am every Sunday morning is a good time to get out the leaf blower, relationships can become strained and when the reasoned and friendly approach has been rejected it is time to Know You Rights according to the law in your state. Warning don’t get involved in a noise war, if they have their stereo blasting all the time don’t be tempted to teach them a lesson with your stereo blasting back, you won't win and you'll become involved in a race to the bottom, and you'll both become the neighbours from hell - be patient do it by the book and the result will in all likelihood be more satisfactory (and legal).
Noise can be difficult to deal with because what one person finds unacceptable another might find quite all right. In the NSW Protection of the Environment Operations Act 1997, The definition of offensive noise in the POEO Act is noise:
(a) that, by reason of its level, nature, character or quality, or the time at which it is made, or any other circumstances:
(i) is harmful to (or is likely to be harmful to) a person who is outside the premises from which it is emitted, or
(ii) interferes unreasonably with (or is likely to interfere unreasonably with) the comfort or repose of a person who is outside the premises from which it is emitted.
The police can and will generally deal with a one off noise problem like a late night party but other persistent and regular noise problems require different remedies that, in NSW, involve contacting the local council to obtain a noise control notice. These notices can cover all types of noise including such things as: noise from animals and from a wide range of appliances, including air conditioners, swimming pool pumps, heat pump water heaters, radios, sound reproduction equipment, musical instruments, power tools, lawn mowers and burglar alarms etc.
The notice can require the noisy activities to be restricted to certain times of the day or certain days. If the notice is not complied with, the council can issue a fine or prosecute. People who receive a notice can appeal against it.
You can take action independently of the local council or other regulator by applying for a noise abatement order under section 268 of the POEO Act. This involves taking you neighbour to court. If the court is satisfied that the neighbour is causing an offensive noise or that the noise is likely to recur, it may order them to stop the noise or prevent a recurrence. If the person fails to comply with the order, they could be prosecuted. The person responsible for causing the noise can appeal against the order. The wise thing to do before you attempt this sort of action is to seek legal advice.
Remember keeping a record by way of a diary can be vital in gaining a successful prosecution.
Update for NSW tenants: A recent decision in the NSW Local Court in the case - Jean Whittlam v Sara Hannah & John Hannah  Downing Centre Local Court 63913/11 – means that landlords can now be held responsible for noise being made by noisy tenants. Mrs Whittlam took proceedings against the owners of the unit for orders pursuant to section 268(4) of the Protection of the Environment Operations Act 1997. The magistrate found that, in this case, the landlord was a person contributing to the noise of the occupier. See these links for more information Sydney Morning Herald, Flat Chat, Owners Bewhare of Noisy Tenants.