Danish Archives are providing digital online records, found by accessing their homepage (link below). Lutheran State Church records, Danish National Census records, and other resources are available online.
In the middle of the page in a grey section is Arkivalieronline. This is the most interesting area I have found. The small pull-down menu area allows you to search for the various records. In my first use I went to Kirkeboger. and then press SOG
it bring you to another selection area.... Select Kirkebøger fra hele landet as this will bring you to the Church Records from around the country.
Then you will need to select a region AMT and a village area. Once there you can determine if records are digitized for the dates in question.