I have found the following links extremely helpful in my genealogy research. The last time that I checked them, they were working, which was on the 11th of  May 2003.

World Wide

• FamilySearch This is the website for the Church of Jesus Christ of Later Day Saints. It features the I.G.I., Ancestral File, Pedigree File and the newly added 1880 Census for the United States and Canada and the 1881 Census for England and Wales. To search these indexes, click on this link. Search for Ancestors
• Cyndi's List This website features many links to over 200000 other genealogical websites on the internet.
• The Federation of Family History Societies
• Cemetery Records Online
• Genealogylinks

Australia

• Australian Commonwealth Government Information
• National Archives of Australia
• National Library of Australia
• On-line Passenger List
• On-line Australasian Names Research Directory
• Brandis, Australian & New Zealand Genealogy
• Australian & New Zealand Genealogy Pages
• Australian Institute of Genealogical Studies Inc. 
• Commonwealth War Graves Commission
• Australian Family Tree Connections
• Web Sites for Genealogist

New South Wales

• New South Wales - Registry of Births, Deaths and Marriages This website contains searchable indexes for births (1788-1918), deaths (1788-1945) and marriages (1788-1945). Use the following link to go straight to the searchable indexes Index Search
• State Library of New South Wales Through this website there is links Internet Resources
• State Records New South Wales this site features Online Indexes including immigration and convict indexes.
• City of Sydney Archives
• New South Wales - Lands Titles Office 
• Society of Australian Genealogists
• Cemeteries in and Around Gunning Shire, New South Wales
• Eastern Suburbs Memorial Park, Sydney
• Indexes to Deaths and Obituaries, New South Wales Newspapers
• The Ryerson Index this site features Indexes of various NSW Newspapers.

Victoria

• Victorian Registry of births, Deaths & Marriages
• Maxi (Apply for Certificate) At this website you can apply for Victorian birth, death & marriage certificates online.
• Public Record Office Victoria Featuring online indexes for Immigration & Probate.
• State Library of Victoria
• Genealogical Society of Victoria Inc.
• Divorce Index Victoria 1861 - 1900 Online Index

Queensland

• Department of Justice and Attorney-General is the Queensland Registry of Births, Deaths & Marriages
• Queensland Government State Archives 
• State Library of Queensland 
• Genealogical Society of Queensland Inc.

South Australia

• Office of Consumer and Business Affairs online ordering of birth, death & marriage certificates
• State Records of South Australia
• State Library of South Australia 

Western Australia

• Registry for Births, Deaths and Marriages
• State Records Office of Western Australia
• Western Australian Genealogical Society Inc. Genealogy WAGS

Tasmania

• Tasmania Births, Death & Marriages
• Archives Office of Tasmania  Tasmanian Family Link
• State Library of Tasmania

North Territory

• North Territory Registry of Births, Deaths and Marriages
• Northern Territory Archives Service

New Zealand

• New Zealand Births, Deaths and Marriages Office
• National Archives of New Zealand
• National Library of New Zealand
• New Zealand Archives - Military Service to 1913
• New Zealand Society of Genealogists
• New Zealand Government Online
• New Zealand GenWeb
• Commonwealth War Graves Commission
• Australian & New Zealand Genealogy Pages

Great Britain & Ireland

• Family Records Portal (United Kingdom) A wonderful place to start for Genealogists with English, Welsh, Scottish and Northern Irish Ancestry.
• UK Online Links to most if not all Government Agencies from  Central Government down to Local Government.
• Commonwealth War Graves Commission For both Soldiers who died while serving in WW1 and WW2 or while serving as part of the occupation forces after the wars
• GENUKI - GENUKI (main index) Content
• The British Isles GenWeb Project
• Guild of One-Name Studies (GOONS)
• Familia Has links to Family History resources in Public Libraries in  Britain and Ireland.

England & Wales

• The National Archives - ARCHON
• Office of National Statistics which holds the English & Welsh B,D,M's (St. Catherine House) & the National Censuses.
• 1901 Census for England & Wales Website features the 1901 Census Online.
• The British Library
• English Workhouses
• The National Library of Wales
• FreeBDM This website has a searchable database of English and Welsh birth, death and marriage registrations which is always being added to and in the future there will be a simular website FreeCEN which will have census information and FreeREG for parish registers, also incompleted.
• Roll Of Honour This website gives quite detailed information on those soldiers that died while serving in the Great Wars. 
• London Metropolitan Archives
• See also Wisbech and the Fenlands for links to website featuring information for Cambridgeshire, Norfolk and Lincolnshire.
• England IGI Batch Numbers

Scotland

• The General Register Office for Scotland The website for the department responsible for B.D.M's and Census for Scotland.
• National Library of Scotland

Northern Ireland

• General Register Office, Northern Ireland
• The Public Record Office of Northern Ireland

Ireland

• The National Archives of Ireland This website feature the online Transportation Records Database

Other places

• Isle of Man Government - Index of Departments
• The State of Jersey