This article is by Klaus Ole Kristiansen with additions by Peter Kurrild-Klitgaard.
See also a note on the national and royal arms by the Danish Ministry of Foreign Affairs.
According to a 17th c. myth, Dannebrog fell from the sky among the Danish forces during the battle of Lyndanisse in Estonia on June 15, 1219. According to some, the Danish levy navy immediately adopted it as its symbol, making Dannebrog the oldest national flag in continued use. However, real proof of use dates back at best to Valdemar IV (king 1340-75). This way Denmark and Austria can both claim the oldest flag, that of Austria being known on seals from 1230.
The square is the national flag, usable by everyone on land and at sea. The swallow tail is the state flag, used by every state institution on land, and by all branches of the armed forces on land and at sea.
Certain institutions have their own flags. Those are generally the swallow tail with some heraldic or other symbol, or some text added. Ships belonging to civilian state institutions that do not have their own flag use the swallow tail with a white crown in the upper field by the hoist.
Her Majesty and the members of the royal family each have their own flags. Certain positions also come with a flag. These flags are all variations on the swallowtail. Except the last three, they all have the symbols in a white square hiding the "center" of the cross:
Many organisations, such as yacht clubs, have special permission to use the swallowtail, some with and some without additional marks. Flag makers can use the swallowtail as a sign of their trade, but only on a horizontal pole.
The dimensions of the square is usually given as one fifth by one quarter of the height of the flag pole. However, the official decree on the flags of trade ships from 1748 is that the white cross be 1/7 of the height of the flag, the rear fields be square, and the two other fields be 6/4 of the length of the rear fields. There was a tendency to make the flag longer, and in 1893 the ministry of the interior stated that due to usage, no objections could be made as long as the front fields where less than 7/4 of the rear ones.
The flag shown here is slightly shorter than this maximum length. Note that the cross is considerably narrower than those of other Nordic flags.
Anyone can fly the square Dannebrog from his/her residence. The flag should fly only during the day, and only on special days. There are a number of official flag days, though they are not mandatory. In addition, you should fly your flag on personal special days, like birthdays, weddings, etc.
Anyone can fly a Dannebrog pennant on land. If you use one, it should fly day and night while the house is inhabited, except when you are flying your flag. At sea the Dannebrog pennant is reserved for the navy.
To the despair of heraldic purists, the Danish state insists on distinguishing between the rigsvåben (arms of the realm or arms of dominion, the arms of Denmark, used by the state) and kongevåben (king's arms, her majesty's personal arms, used only by the royal house).
The arms of dominion of Denmark are: Or three lions passant in pale azure, a semy of water lily leaves gules. Danish heraldry distinguishes between patterned and sown. This field is sown with leaves. That means that no leaf is cut by the edge of the shield or partially obscured by a lion.
While there are good reasons to believe that Valdemar I (king 1157-82) may have used the arms, it is not known until the time of his son, king Knud. There has been some debate among Danish armorists on this question, especially what the symbolism of the three lions might be, but since a study published in 1984 by Nils G. Bartholdy, there is now unanimous support for the fact that the arms are unknown before ca. 1194.
The modern version is:
The arms of Slesvig are of course a diminutive of Denmark. Slesvig was a fief created as a defensive measure, and held by a close relative of the king until the time of king Abel's sons. The arms of the Union symbolize the Union of Kalmar, which consisted of Denmark, Norway, and Sweden. The arms of the Faroes(whose name means Sheep Islands) are canting.
Having mentioned the arms of Her Majesty's father above, I'd better describe them too.
Frederik IX was "by the grace of God king of Denmark, the Goths, and the Wends, duke of Oldenborg, Slesvig, Holsten, Stormarn, Ditmarsken, and Lauenborg". Margrethe II styles herself "by the grace of God Queen of Denmark". Most of the changes reflect this difference. Her Majesty kept Oldenborg, her family arms, and Slesvig, part of which is still part of Denmark.
The arms of the Goths are fictional. The wyvern as been considered since the 14th c. as a symbol of the Slavs and the people in the South-West Baltic; but the title of king of the Wends has been notional since the 14th c. The arms of Holsten are rather special. They are usually blazoned "A nettle leaf" in Danish. It doesn't look like one, though. The original arms were: Argent a bordure indented gules. At some time, this was reinterpreted as a white charge on a red field, and blazoned Gules a nettle leaf argent. However, the emblazon has now changed considerably. Woodward's Treatise blazons it as: Gules an escutcheon per fess argent and of the field, between three demi-nettle leaves and as many passion nails in pairle of the second.
Most heirs to the throne now use the royal arms, only with a different crown. Until 1953, the members of the Greek royal family as princes of Denmark were potential heirs to the Danish throne and as such used a combination of the Danish and Greek royal arms. (They ceased to be potential heirs at that date, when succession was limited to the descendants of Christian X). Also, currently the second son of the present Queen Margrethe II, HRH Prince Joachim, has adopted an arms which is differenced from that of the royal arms proper by including a field for his paternal family, the French family of Monpezat. There is a special crown for the crown prince, and another for the others.
For styles of Danish princes, see the page on Styles and Precedence.