The relationship between the United Kingdom and the USA.
The Special Relationship is the name given to the close Anglo-American military, political and trading alliances that have been evident throughout most of the 20th century and continue into the present century. The overlapping language and culture and the large amount of immigration into the USA from the British Isles are other factors that go some way toward explaining this relationship. The first person to make these ties concrete by giving them a name is generally regarded to be Winston Churchill, in his Sinews of Peace Address at Westminster College, Fulton, Missouri, in March 1946 (more commonly called the Iron Curtain speech):
I come to the crux of what I have traveled here to say. Neither the sure prevention of war, nor the continuous rise of world organization will be gained without what I have called the fraternal association of the English-speaking peoples. This means a special relationship between the British Commonwealth and Empire and the United States.
Churchill did coin the phrase, but in fact he had already used it before that speech. The New York Times Herald reported a quotation from in November 1945:
"We should not abandon our special relationship with the United States and Canada about the atomic bomb and we should aid the United States to guard this weapon as a sacred trust for the maintenance of peace."
The specialness of the two counties' relationship has endured, although it has been rather cool at times, particularly when the personal relationship between US President and the British Prime Minister wasn't strong. Whilst the degree of closeness between the nations is largely determined by judgments of mutual political, military and trading benefits, the personal factor has always had a strong influence. It has always been a chicken and egg situation and it frequently hasn't been clear which has come first - policy or friendship; for example, it is reported that Bill Clinton and John Major didn't like each other and it is the case that the period of their time together in office didn't result in especially close ties between the two nations. It is also reported that Lyndon Johnson and Harold Wilson were rather distant with each other at a time that the British government refused to support the USA over Vietnam.
The coining of the term came about soon after WWII when Churchill and Franklin Roosevelt had developed a close working relationship. How well they liked each other personally isn't well recorded, although in the numerous photographs of them taken at the Yalta conference they seem to be enjoying each other's company. Mind you, like the old joke about what difference there might have been if Khrushchev had been shot rather than JFK - "I doubt that Mrs. Khrushchev would have married Aristotle Onassis", they appear quite pally with Stalin is those pictures too - and neither country opted for a special relationship with the USSR.
Other times when the special relationship has flourished are during the periods in office of Harold Macmillan and John F. Kennedy and of Margaret Thatcher and Ronald Reagan.
More recently the relationship, although on the face of it an unlikely one, between Tony Blair and George Bush has been particularly close. While visiting Britain in 2003, George Bush said in a speech that Britain was America's "closest friend in the world". He is also on record as saying, in 2001, that "We have no greater friend than Mexico" and, in 2002, "We have no better friend than Canada". History doesn't record who his best friend was in 2004.
The imbalance between the relative power of the two nations has always made the relationship one-sided and occasionally Britain has been made to appear rather subservient. The acceptance of the Bush regimes' policies by Blair, especially over Iraq, has resulted in some criticism of the British Government in the UK and a feeling that Britain should distance itself from the USA. A poll published by The Guardian newspaper in 2006 said that 63% of Britons felt that Britain is tied too closely to the USA. Blair has been satirized and portrayed as Bush's poodle. The Iraq War is unpopular and his apparent desire to follow whatever initiatives have been taken by the USA is widely seen as the reason for Blair's political downfall.
Nevertheless, the special relationship continues.