Copenhagen (Danish: København; Latin: Hafnia; French: Copenhague) is the capital of the Kingdom of Denmark. It is also the city of residence for the kings and queens of Denmark.
Located in a favourable position by the narrow Sound, which is the most accessible passage from the Baltic to the North Sea (by way of Kattegat and the Skaw), and gifted with a natural harbour, Copenhagen has been a major mercantile center since mediaeval times. Until the mid-19th century, Copenhagen shipping dominated Nordic trade, and the city is still home to several of the world's largest shipping companies.
Nowadays, Copenhagen is a lively, active city, with plenty of tourist attractions and night life. Among the more well-known attractions are the amusement parks Tivoli and Bakken, the statue of The Little Mermaid, and Kastellet, the Citadel of Copenhagen. For more tourist attractions, see my Noder's guide to Copenhagen.
Population (Jan. 1, 1999):
Copenhagen proper: 491,082
With environs: 1,192,912
Addendum:
After having read nine9's otherwise excellent writeup, below, I am reminded that perhaps a mention of Copenhagen's eventful military history is in order. Since it is rather difficult to sum up a thousand years of history in a few paragraphs, I'll restrict myself to mentioning the four most significant military events in Copenhagen's history:
1658: The Siege of Copenhagen
At the culmination of a protracted war between Denmark and Sweden, Copenhagen remained essentially the only unconquered part of Denmark. A lenghty siege (with the Danes receiving relief in the form of supplies and reinforcements from Dutch fleets in the Sound) ended in a settlement (the Peace of Roskilde) which left most of Denmark free, although significant concessions were made to the Swedes, including all of Scania.
1801: The Battle of the Roadstead of Copenhagen
(Danish: Slaget på Reden). As part of a British plan to neutralise the possibility of Danish naval intervention in the wars with France, a British fleet
under Sir Hyde Parker met and inflicted a significant defeat on the Danish navy. After the prince regent (later King Frederik VI of Denmark) made the ill-advised decision to give up the fight, the remaining Danish ships were scuttled or seized as prizes by the British.
1807: The Bombardment of Copenhagen
After the defeat in 1801, the hitherto-neutral Denmark joined the French side in the Napoleonic Wars, and this led to a siege of Copenhagen by a British army, in 1807. The siege included a new development in military strategy: the world's first deliberate terror bombardment of a civilian population (in fact, it is reported that when "Bomber" Harris discussed the decision to terror-bomb Dresden during WWII, he used the expression "We'll Copenhagen them!").
1940: The German Occupation
As part of Operation Weserübung, the German Wehrmacht executed a well-planned surprise attack on strategic locations in Copenhagen, using troops hidden aboard a "Trojan horse" ship in Copenhagen's port. The Nazi occupation lasted until May 1945.