First Day Covers were first used in 1941 in connection with a serie of 3 stamps for the 200 year day of the death of a Danish adventure traveller Vitus Bering.
Nearly all Danish stamps since the stamps for Bering have been first day cancelled. The main exception are some of the standard stamps.

None of the Danish First Day Covers are rare. The number of first day covers have never been below 10.000 and the highest number was reached in the seventies, when some first day covers were made in close to 100.000 cancellations.
At the moment the number of FDC are much lower than in the sixties and seventies but still well above 10.000.
It is hard to put prices on Danish FDC as they are often sold to prices that are below the original price of the stamps. With a lot of patience it should be possible to get most of the FDC at prices as low as 1 to 2 Dkr a piece - or close to 0.20 €. Exceptions to these prices are mainly the first FDC from 1941 to 1946 and the newest FDC issued after the late nineties. They can be traded at higher prices.

Some of the less common newer stamps have been removed from the original envelope and sold as single cancelled stamps. Normally these stamps are not as popular among the buyers as stamps cancelled the normal way. The practise of using stamps from first day covers as cancelled stamps is common with stamps from Greenland.
An example of this is Greenland #gr78. This stamp is more commen cancelled with a first day cover cancellation than by any other legal cancellation. Most collectors of cancelled stamps prefere stamps cancelled for daily use.