Noder's note: The following should be viewed partly as a rejoinder to Glowing Fish's writeup, above, and as clarification of the actual circumstances. I will not quibble with GF's glowing paeans to American ingenuity, though I personally find them slightly overstated - certainly, the American achievements in Greenland were "remarkable", though in a different sense than GF implied, and for different reasons than might be immediately apparent. Overall, GF got the facts mostly right, but somehow missed the point.
Let's start with some background. On April 9, 1940, as part of the German Operation Weserübung, Denmark was overrun by German forces, and a concerted effort to invade Norway was undertaken.
At the time of the invasion, Greenland was a long-time colony of Denmark, governed, under the terms of the Greenland Act of 1908 (Grønlandsloven af 1908), directly from Denmark, but with significant input from two regional councils, landsråd, at Godthaab/Nuuk and Godhavn/Qeqetarsuaq. The heads of these two councils, and much of their staff, were Danes.
In Washington, D.C., the Danish ambassador, Henrik von Kauffmann, reacted to the occupation by (illegally) declaring himself the sole legal representative of Denmark. It has later been conjectured that he did so in connivance with the U.S. State Department, which saw clear benefits in such a development. At any rate, Kauffmann's declaration was accepted at face value by the State Department, with unbecoming alacrity. Effectively, this meant that the U.S. Government had declared Kauffmann de facto dictator of all unoccupied Danish dominions. There is no way that the U.S. State Department can have been unaware that Kauffmann did not have the authority that he represented himself as having, and the conclusion must be that they acted deliberately, and in bad faith.
As GF notes, Greenland was of enormous strategic importance. Not only as an "unsinkable aircraft carrier" (and during the later phase of trans-Atlantic convoying, as a vital way station for airplanes and ships), but also for a much less obvious reason: meteorology. Much of the weather over northern Europe forms off the East coast of Greenland, and if for no other reason than to deny the Germans access to accurate weather forecasting (e.g. for planning a cross-Channel invasion of England), Greenland had to be secured.
It is not surprising therefore, that the U.S. State Department did not look too carefully at Kauffmann's legitimacy when he signed a treaty (an act which, I remind you, no ambassador is usually empowered to undertake - and which would have to be ratified by his national legislature, afterwards, before coming into effect) granting unlimited U.S. access to Greenland. Not for the duration of the war - but indefinitely. This was, in effect, an American seizure of Danish territory by force, and in circumstances of very questionable legality, to say the least.
Denmark's liberation came, after five long years, on May 5, 1945. All over Greenland, the Danish flag Dannebrog was flown, and people walked about the streets calling out "Danmarkigooq aniguisitaavoq!" ("Denmark has been liberated!"). Unlike a later generation (see note below), the Greenlanders of the 1940s very much considered themselves to be Danish, if not actual Danes. They were loyal and eager for things to return to the status ante quo. So it was not to be.
For eminently practical reasons, Greenland was still a strategic location - although the reasons were new. With Nazi Germany defeated, a new enemy loomed, and the Cold War was begun. With the shortest distance between the Union of Soviet Socialist Republics and the United States of America being across the North Pole, Greenland was suddenly America's first line of defense - and they were in no way prepared to relinquish such a significant strategic position.
Enter the diplomats. America and Denmark had a common cause in the post-World War II era, along with the rest of NATO - balancing the Soviet threat to European and American security with a sufficient deterrent. Although Kauffmann had completely exceeded his authority (to the extent where one is strongly tempted to speak of treason), and was fired, the Danish bicameral parliament of the time was not inclined towards subsequently disavowing the treaty, so they merely ratified it, with no revisions. The Danish Government later negotiated a revision/ratification of the treaty, which took effect on June 8, 1951, and which included a secret codicil giving the U.S. blanket permission to station nuclear weapons on Greenland - a secret that was officially denied by all parties until the late 1980s.
The presence of nuclear weapons at the U.S-operated Thule Air Base led to one of the nastiest accidents in the history of nuclear weapons, when a nuclear-armed B52 crashed on the base runway. The subsequent cleanup was undertaken by Danish and Greenlander personnel, who were not informed of the radiation hazards, with predictable results. The residue of the crash was dumped into the ocean near the base.
I will close by taking serious issue with one thing that GF wrote. I quote: "The influx of American technology and supplies would mark the introduction of Greenland into the modern world."
This is arrant nonsense - it did no such thing. Greenland was already modernising, albeit slowly, and the great changes in Greenland's "modernity" (a detestable term, that smacks of cultural imperialism when used in these circumstances) were undertaken during the 1960s and 1970s, and were not in any way connected with American military presence - truth be told, they were motivated by the ever-present profit-motive: the creation of a generation of educated Greenlanders, suitable for employment in middle-management positions in the increasingly centralised cannery industry. The result, unsurprisingly, was a disaffected generation that demanded, and in 1979 achieved, home rule.