The majority of Australian records are held at State level, so you need to know where your family was.
Commonwealth Sites
History of Australia – Wikipedia
Map showing states and date of creation
National Archives of Australia – includes military records
Commonwealth war graves site
Convicts transported to Australia – a guide
Australian newspapers 1803 – 1954 – National Library of Australia
Australian Cemeteries Index
Another Australian Cemeteries Index
Third Australian Cemeteries Index
See also Find A Grave and Billion Graves
Society of Australian Genealogists
NSW
NSW Registry of births, marriages and deaths
NSW State Archives and Records – includes convict records
Queensland
Queensland births, marriages and deaths
Queensland Genealogical Society
Advice, indexes and services focused on Queensland
Useful links focused on Queensland
South Australia
Registry of births-marriages-deaths for South Australia
South Australian genealogy and heraldry Society
South Australia genealogy links
Cemeteries of South Australia
Tasmania
Registry of births, marriages and deaths
Useful links for Tasmania
Family History Society
Tasmanian Archives
Victoria
Registry of births, marriages and deaths
Genealogy links
Ballarat & District Genealogical Society
Western Australia
Registry of births, marriages and deaths
Western Australian Genealogical Society