Genealogy on the Cheap - Select Links to Archives and Registries (Feb. 2018) (All links open a new window)
Danish State Archives
The Danish State Archives Filming Centre digitizes parish registers and population censuses in order to make them accessible via the Internet. The Archives also has an online Danish Demographic Database that is the obvious choice if you wish to search for your ancestors online via the State Archives.
England and Wales
The National Archives
The TNA not only has helpful guides to research, but also has a variety on online collections, including military and probate records. Some are free to view the actual record and others are not.
General Register Office Online Index
This website requires registration, which is free. It is free to search the indexes, which include registrations of births up to 1917 and deaths to 1957. One big advantage is that you can search by, or see, the mother's maiden name on all registrations (not just those after Oct. 1911). Also, the age at death on registrations prior to 1866 is given. From this site, you can order a digital copy of the actual registration at a reduced price (£6.00 vs £9.25).
Irish Genealogy Portal
A website operated by the Department of Arts, Heritage and the Gaeltacht. Search multiple online sites from one place. Searchable records include church, civil registration, census, property, migration, military, gravestones, and more. Results of church register and civil registration searches often include a link to images.
National Archives Ireland
National Archives Genealogy Website home page. Links to free census, land, military, and probate indexes and/or records. More was added in September 2016 and they continually add records.
Direct link to searchable index and census records are available for 1901 and 1911 (also 1821, 1831, 1841, 1851 census fragments).
Public Record Office Northern Ireland (PRONI)
https://www.nidirect.gov.uk/proni - Take the link 'Search Archives Online'
Several online indexes including the Freeholders’ Records, Ulster Covenant and Will Calendars. The site has search capabilities and the images are free.
General Register Office Northern Ireland (GRONI)
Search the civil registration indexes for N. Ireland for free (if you have at least one credit - £0.50). Includes births over 100 years, marriages over 75 years, and deaths over 50 years. Pay one credit for enhanced index and five credits for full record or image.
Canada (General) http://www.bac-lac.gc.ca/eng/discover/Pages/browse-product-type.aspx#databases
Library and Archives Canada - online databases of census, land, immigration, etc.
Provincial Archives of Alberta - online indexes of births 120+, marriages 75+, deaths 50+ years. $0.35 per page for a copy and they will mail them for a small handling charge.
British Columbia http://search-collections.royalbcmuseum.bc.ca/Genealogy
Royal BC Museum - Search their indexes to births (1854-1903), marriages (1872-1941), deaths (1872-1996), colonial marriages (1859-1872) and baptisms (1836-1888). Many of the results link to an image of the registration.
The Manitoba Vital Statistics Agency provides online indexes of births 100+, marriages 80+, deaths 70+ years. A copy can be requested for a fee.
New Brunswick http://archives.gnb.ca/Archives/
The Provincial Archives of New Brunswick features a federated database search where the user can search 37 databases at once, which include births, marriages, deaths, cemeteries, directories, and more. Many of the results show the image of the record. Digitized copies are free to download. If not digitized, the film number is given and can be used for Inter-Library Loan (ILL).
Nova Scotia https://www.novascotiagenealogy.com/
Nova Scotia Historical Vital Statistics - Indexed historical records of births, marriages and deaths. Index and images are free to view, but a fee is charged for copies.
FamilySearch Historical Records https://www.familysearch.org/search
Many state archives records have been filmed and indexed on FamilySearch. If you can't find it there, then check to see if the state has its own index.
Just to name a few...