Egypt and Syria joined together and formed the United Arab Republic, but it was short lived only lasting from 1958-1961.
Just before the fall of France in 1940, the British war cabinet proposed an "indissolulable union between France and Britain". Churchill hoped that the display of solidarity would encourage the French to continue a guerilla war from their colonies, which would have the vital impact of securing the French fleet for the Allies. The French cabinet rejected the offer, seeing it as an arrangement by which the British would steal their fleet and colonies, and decided to sign the terms which Germany gave them. Although the proposal was a failure, it is an example of two sovereign nations actually discussing a union which would result in shared currency, citezenship, and defense and foreign policies.
My source is
"Their Finest Hour" by Winston Churchill
The United Arab Republic (UAR) is probably one of the more obvious examples. This was a union between Egypt and Syria from 1958-61.
The initiative for the move came from Syria. The country had been undergoing severe political turmoil in the post-war period - five coups between 1947 and 1955 - and political actors were increasingly despairing of a domestic solution to their problems. The Ba'ath Party (still ruling Syria but better known in the West for its Iraqi branch) was strongly pan-Arabic in outlook and began to cast around for a strong foreign ally.
That they chose Nasser's Egypt isn't a surprise. Post-Suez (and pre-Yemen or 1967) Nasser was at the peak of his popularity. Head of a modernising military regime, with a strong anti-imperialist record, his radio broadcasts (Voice of the Arabs) were immensely popular throughout the Middle East. If his pan-Arabic was primarily rhetoric then the opportunity to rule Syria at least offered the opportunity to cement Egypt as a regional, if not global, leader.
So in January 1958, without any warning to its government, the Syrian army leadership flew to Cairo and began negotiating for a union. Initially the talk was of federalisation but Nasser's terms were for an absolute union. Under pressure from its army, the Syrian government accepted.
But this puts into question the definition of a 'single nation'. The UAR was united at a political level but never as a unitary state - Nasser presided over an all-union cabinet on foreign affairs, defence, etc but two regional cabinets existed in Cairo and Damascus. And there were clear limits on how far integration could go: Egyptian efforts to export its economic model (ie nationalisation, high-taxation, land reform, etc) met with sharp Syrian resistance.
This highlighted the biggest grievance with the union: it was less a meeting of equals and more an imposition of Egyptian institutions and policies on Syria. The Syrian military and intelligence services were rendered subservient to their Cairo counterparts and all political parties (including the Ba'ath) were dissolved. Into the mix came a number of personality clashes - particularly Abdel Hakim Amer, Nasser's representative in Damascus, and Abdel Hamid Sarraj, Syrian intelligence supremo - and relations quickly soured.
Events came to a head in early 1961. By then Nasser, who had thoroughly underestimated the challenge of ruling Syria, had managed to alienate both the Syrian political elite and its military. The latter was, again, the key ac tor. On 28 Sept 1961 the Syrian army staged a coup, expelling the leading Egyptian representatives from the country the next day.
That wasn't entirely the end of that - Egypt didn't formally abandon the UAR until 1971 - but increasingly bitter relations between the two countries precluded any rapprochement.
Sources:
Cook, The Struggle for Egypt
Rogan, The Arabs: A History
what England and Scotland? What about the united states? What about the Swiss cantons? Did this ever happen in China?