Hi Liz,

The index online to NSW Registry of Births, Marr., Deaths has deaths to 1976:
http://www.bdm.nsw.gov.au/cgi-bin/Index/IndexingOrder.cgi/search?event=births

and marriages to 1956:
http://www.bdm.nsw.gov.au/cgi-bin/Index/IndexingOrder.cgi/search?event=marriages

Births only to 1906.

- But each State has its own records, and most are not online.

Victoria is online but not free, like NSW.
http://online.justice.vic.gov.au/servlet/bdm_home

Other Australian free websites for the 1900s where you can sometimes pick up useful genealogical information are:
http://www.access.prov.vic.gov.au/public/PROVguides/PROVguide023/PROVguide023.jsp
[Public Record Office, Victoria]

This one is not as useful, because mostly 1800s:
http://www.records.nsw.gov.au/archives/indexes_online_3357.asp
[State Records NSW]

http://www.naa.gov.au/the_collection/recordsearch.html
This is the site of the National Archives [for all Australia] - you can choose to search as a Guest. It includes next of kin in war records, and "Application by British migrants for assisted passage". You get the best results by putting in as few key words as possible. If a name, don't add anything else.

For New Zealand, this has 1900s records:
http://www.archway.archives.govt.nz/
[Archives NZ - use Simple Search]

http://freepages.genealogy.rootsweb.com/~shipstonz/cemeteries.html
[NZ cemetery records]

B/D/Ms are not online, but are published on microfiche and held in many genealogical libraries.

I have a NZ Soc Gen CD index which includes marriages to 1934 if you would like me to check that?

Sue