Further links/information may be added over the years, so it's worth checking this post every so often just in case a new link is the one that solves a brickwall. New stuff will usually be added at the end.

A good place to start is Genuki, as this lists the towns and villages in Dorset, as well as giving other links.
https://www.genuki.org.uk/big/eng/DOR

Next is the Jurisdictions on FamilySearch, where you can see the relationship of the various parishes to each other. Note that these refer to 1851, and some parishes may have changed since then.
https://www.familysearch.org/mapp/

Never underestimate the local Family History Society. Some offer (limited) research services; many have publications for sale which can considerably reduce your research time if you invest a tenner. Many FHSs now have their baptism/marriage/burial indexes on Findmypast or Ancestry, but other indexes can exist so check out the Society's website. It can also be worthwhile joining a FHS, because some have a member's-only section with indexes not available elsewhere. (In addition, you get journals three or four times a year. )
https://www.dorsetfhs.org.uk/

FamilySearch has some PR images online for some Dorset parishes under the dataset England, Dorset, Paris Registers 1538-2001. Instead of searching for a name, scroll down the page a little and click on the 'browse' link.

FMP has PR transcriptions for baptisms, marriages, and burials. On each page there is a link to a parish list which tells you which parishes are included and for which years. Remember that some years may be missing because the PRs for those years no longer exist but the coverage list may not reflect this.

Other datasets on FMP are
Dorset Hemp and Flax Growers
Dorset Memorial Inscriptions
Parish apprentices for Dorset
Somerset & Dorset Notes and Queries, 1890-1980

PR transcriptions available for free can be found at https://www.freereg.org.uk/
Please note that coverage is not 100% complete.

Ditto coverage with free census transcriptions at https://www.freecen.org.uk/
As at 23 Dec 2019 the coverage is
1841 - 63.2%
1861 - 26.7%
1871 - 14.1%
1891 - 28.9%

The 1881 census transcriptions are available for free at both FMP and Ancestry.

Datasets available on Ancestry include (both with images)
Dorset, England, Poor Law Settlement and Removal Records, 1682-1862
Dorset, England, Poor Law Apprenticeship Records, 1623-1898
The following have PR images, though I haven't checked how complete the coverage is. There is a drop-down list of parishes which can be compared to the list of towns and parishes in Genuki.
Dorset, England, Church of England Baptisms, Marriages and Burials, 1538-1812
Dorset, England, Church of England Marriages and Banns, 1813-1921
Dorset, England, Church of England Births and Baptisms, 1813-1906
Dorset, England, Church of England Deaths and Burials, 1813-2010
Dorset, England, Church of England Confirmations, 1850-1921
There are transcriptions for a few parishes 1500s - 1812 in
Dorset, England, Extracted Church of England Parish Records (list of parishes at bottom of page)

Dorset, England, Tithe Apportion and Maps, 1835-1850
Dorset, England, Electoral Registers, 1839-1922
Dorset, England, Wills and Probates, 1565-1858
Dorset, England, Quarter Sessions Order Books, 1625-1905
Dorset, England, Poor Law and Church of England Parish Records, 1511-1997
Dorset, England, Militia Lists, 1757-1860
England, Select Dorset Church of England Parish Registers, 1538-1999
Dorset, England, Convict Transportation Records, 1724-1791
Dorset, England, Vagrant Passes 1739-1791
Dorset, England, Land tax returns 1780-1832
Dorset, England, Jury lists 1825-1921
Dorset, England, Calendars of prisoners 1854-1904
Dorset, England, Crew lists 1863-1914
Dorset, England, Bastardy records 1725-1853
Visitation of Dorset 1623

Both FMP and Ancestry will have other records which include Dorset (e.g. Owners of land 1873) but I've listed only ones which have Dorset in the dataset title.

Either or both of these subscription sites may be available for free at your local library. Both of them are available to search for free (though you may have to register), and you can also take out a free 14-day trial though remember to untick the auto-renew subscription box otherwise you will find your bank balance goes down with a big bump.

Burials in Blandford Forum cemetery from 16 June 1856 to 6 July 2010 are available at Deceasedonline (dot com), a subscription site.

Pam