This is an ongoing list of websites where you can search for data; the ones listed here are free.
Commonwealth War Graves Commission (CWGC) has a casualty database listing the names and place of commemoration of the 1.7 million men and women of the Commonwealth forces who died during the two world wars. You can search by casualty or by cemetery, download the results as a spreadsheet, and keep the details of each casualty as a .pdf. http://www.cwgc.org/find-war-dead.aspx
Family Search is a website that has been developed by the Church of Jesus Christ of Latter-Day Saints (LDS). With its worldwide coverage, it can be the starting point for any search, and it is also full of helpful information in the Wiki, e.g. maps of historical parishes, and many many other things: https://familysearch.org/.
Family Search includes the International Genealogical Index (IGI). Here are two sites that make it easier to search the IGI: Steve Archer’s http://www.archersoftware.co.uk/igi/index.htm and Hugh Wallis’s original list: http://freepages.genealogy.rootsweb.ancestry.com/~hughwallis/IGIBatchNumbers.htm#PageTitle
Find A Grave helps you trace cemetery records; it is particularly strong on Canada, England, and the United States – but many countries are included. For instance, there are currently (June 2016) 229 records for EZARD – 42 in England, of which 23 are in Philips Park Cemetery in Manchester. Find A Grave.
FreeBMD for transcribed entries from UK birth, marriage and death registers from 1837 to 1983: www.freebmd.org.uk
FreeREG is the place to check for transcriptions of baptism, marriage, and burial entries in parish registers. The search page now has a new look. http://freereg2.freereg.org.uk/
FreeCEN for transcribed entries from UK censuses 1841-1891. You need to check which counties have been done. www.freecenorg.uk
Online Parish Clerks (OPCs) transcribe old parish registers and make the transcriptions available online. County coverage can be patchy, and within a county not all parishes are covered. The Lancashire Online Parish Clerks have made many thousands of records available to search online: http://www.lan-opc.org.uk/
Public Profiler, a project from University College, London, is a world family name mapping website. http://www.publicprofiler.org/
UK Genealogical Directories and Lists on the Internet: http://www.ukgdl.org.uk/
Many of the organisations that hold original records have partnered with commercial bodies, e.g. Ancestry, Find My Past. Digitised records can then be viewed, for a fee, on the commercial site. No site offers all the records, so before taking out a subscription you need to check the datasets available and how relevant they are to your own researches. I use subscription sites on an ‘as-and-when’ basis, e.g. a short-term/discounted sub or ‘free’ days.