Denmark guide
Start with FamilySearch Denmark Genealogy wiki for great research information and links to useful sites:
Search for your Danish ancestor's birth/baptism/marriage/burial records either via indexes, or scanned parish registers.
The Danish collection also includes scans of deed and mortgage registers and estate records including probate records.
https://familysearch.org/search/collection/location/1927025?region=Denmark
Danish Demographic Database
Search for transcribed census records from 1787 to 1925
http://www.ddd.dda.dk/soeg_person_selv_en.asp
Danish State Archives - Arkivalieronline. Here you will find digitised parish registers, census records, probates, and various other scanned records, free.
https://www.sa.dk/brug-arkivet/ao/arkivalieronline
The Danish State Archives – online services
Excellent information on getting started, basic records, Danish names, handwriting and a dictionary of common words. In English.
The Danish Emigration Archives
Search emigration records for nearly 400,000 Danes who emigrated between 1869-1908. For 'Australia' type 'Australien'.
Search engine for people from the counties of Odense, Ribe & Svendborg for fæsteprotokoller (copyholder agreements) and skifteprotokoller (probate) registers. Find your ancestor here and it will direct you to the appropriate scanned register and page number.
https://navneregistre.dis-danmark.dk/faeste_skifte/index.php
Danish feast day calendar from the year 1500. Useful for those parish register entries where the date is recorded as a feast day.