Australia

Each state has it's own educational laws. There is a fairly new Australian wide Home Education Association that has been formed  http://www.hea.asn.au/
 
There are various interpretations to laws in different states and many various opinions on whether to register with the state Board of Studies or not to register. I live in the state of New South Wales and I do follow the states key learning areas and I do have a Scope and Sequence to present to the officer who comes to the home for registration purposes. I would say only one third of homeschoolers I know of are actually registered, the others are technically illegal but they do not see it that way. The more casual your approach to homeschooling and the less one follows key learning areas and maintains records of some sort the more hassles one would have in registering. The maximum registration period they give in this state is 2 years then I have to reapply. To my knowledge you can home educate in every state but Queensland has the toughest laws ( most home educators that I have heard of homeschool without registering in that state). It is fairly easy in my state and easiest in Australian Capital Territory. 
 

New South Wales

The official site from the NSW government...
http://www.boardofstudies.nsw.edu.au/parents/pdf_doc/home_ed_info_package.doc

Tasmania

Here is a site with information about what you need to do for Tasmania. It is just a summary without the official guidelines.
http://www.tased.edu.au/tasonline/theac/

Information on this page should not be considered legal advice.