The Danish reference frame currently in use is a realisation of the European Terrestrial Reference System 1989 (ETRS89).
Older data was typically referred to the European Datum 1950 (ED50).
Plane coordinates: UTM and DKTM
In Denmark, the primary plane coordinate system for mapping and planning is the Universal Transverse Mercator, UTM, referred to ETRS89. But as the Danish land mass crosses the border between two UTM zones (32 and 33), there are often slight adjustments to the formal UTM definition.
Formally, zone 32 ends at 12E, west of Copenhagen; but zone 32 is often also used for the entire group of islands surrounding Zealand, leaving only Bornholm and its archipelago in zone 33.
The relevant EPSG codes are EPSG:25832 (UTM zone 32, ETRS89) and EPSG:25833 (UTM zone 33, ETRS89).
For building and construction work, the DKTM system is recommended, as it has a smaller scale factor than UTM. The DKTM zones are narrower than the UTM zones, so they represent better local fits to the actual landscape, and their corresponding false northings have been designed to make it easy to discern between coordinates in different zones.
The relevant EPSG codes are EPSG:4093 (DKTM zone 1, ETRS89), EPSG:4094 (DKTM zone 2, ETRS89), EPSG:4095 (DKTM zone 3, ETRS89), EPSG:4096 (DKTM zone 4, ETRS89).
Older cadastral data is typically given in System 34 (System 45 for Bornholm). These systems are not supported in the EPSG registry.
The Danish vertical reference frame currently in use is DVR90, Danish Vertical Reference 1990.
Older data was typically referred to DNN (“Dansk Normal Nul”), or to local vertical reference systems.
The relevant EPSG code is EPSG:5799, DVR90.
Note that the EPSG registry also supports compound coordinate systems, based on the joint use of (DKTM, DVR90) and (UTM, DVR90).
The currently valid transformations between/to/from Danish geodetic systems are implemented as parts of the PROJ library, through the geodetic parameter files available from the proj-data package. The source material for the Danish transformations in proj-data is maintained as part of the “Nordic Geodesy” parameter collection.
PROJ and support for proj-data is, however, built into a wide range of geospatial software, so unless you are a software developer or integrator, you will most likely not need to download anything in order to have access to the current Danish transformations.
Until 2013, the official Danish transformations were implemented in the transformation library trlib, and its graphical user interface companion KMStrans2. While unsupported, KMSTrans2 is still available: Follow the instructions given here, using the program files and the supplementary data files. Note, however, that this material is unsupported, and not updated since 2013.
The EPSG geodetic registry.