My home province, Newfoundland (now Newfoundland and Labrador) refused to join Canada in 1869, and by 1933 it had Dominion status equal to its larger neighbour. Then came the Depression, and Newfoundland - already deep in debt from the cost of building a railroad across the island, and sending the Royal Newfoundland Regiment to fight in the First World War - came close to bankruptcy. A British-appointed "Commission of Government" took over governance of the island and Labrador.

Newfoundland did pretty well for itself during the Second World War, with money flowing in from the American, Canadian and British military presence. With the former Dominion better able to stand on its feet, a referendum was held with three choices - a return to independence, joining Canada and continuing with the Commission of Government. Only a small minority opted for the third option, so a run-off between Responsible Government and Confederation was held later that year. This time, a small minority - 52% to 48% - chose to become a Canadian province.

There are a few examples throughout history of a country submitting voluntarily to the "protection" of another power, becoming a protectorate and thus losing part of their sovereignty. Hyderabad in India is the first thing that comes to my mind, in the late 1700s it was being continually raided by the Marathas and Mysore (the power major native powers in India at the time) and voluntarily became a protectorate of the expanding British East India Company to gain their military assistance. This was a crucial factor in allowing the British to penetrate the interior of India and envelop Mysore. Armenia actually did submit to Mongol protection after seeing what they did to Baghdad and the Seljuk Turks.

There must be more examples besides those, too. As for countries surrendering complete sovereignty, I can't think of any, but that doesn't mean it didn't happen. The independent city-state of Timbuktu did peacefully join the Mali Empire in the 1300s, but I don't know about it happening to entities larger than cities.

Sources: The Cambridge History of India The Encyclopedia of Mongolia and the Mongol Empire by Christopher P. Atwood A Short History of West Africa 1000AD-Present by T.A. Osae, S.N. Nwabaro, and T.A. Odunsi

One can argue that this happened between Georgia and Russia in the late 18th century. The 1783 Treaty of Georgievsk was signed by the Russian Empire and the Kingdom of Kartli-Kakheti (eastern Georgia), which effectively made the Georgian kingdom a protectorate of Russia, which included giving the Russian Tsar the authority to confirm the kings and heirs of Georgia. King Erekle II (who signed the treaty) died in 1798, succeeded by his son Giorgi XII, who in turn died in 1800; Giorgi's sons fought over the succession, and as a result Tsar Paul simply declined to authorise a successor, effectively annexing the kingdom (Imereti, the western Georgian kingdom, was incorporated into Russia in 1810).

How this can be seen as Georgia joining Russia? Well in Soviet historiography the Treaty of Greorgievsk was seen a fraternal friendship, the first such act between the Russians and Georgians. Even before the outright annexation, Georgia had effectively given up its independence and sovereignty to Russia, ostensibly to help protect it from attacks by the Ottomans and Persians (in fact a Persian attack in 1795 showed the Georgians that the Russians were not interested in abiding by the terms of the treaty). It was not really that unique, as various Georgian kingdoms had had similar agreements with the Turks and Persians in the centuries prior, allying with whomever would best protect their interests. But this treaty was the one that brought in the Russians, and was voluntarily signed by Erekle II, and did lay the basis for nearly 200 years of Russian occupation.

Attalus III, the last king of Pergamon, a Greek kingdom in modern day Turkey, upon his death willed his kingdom to the Roman Republic in order to avoid a succession crisis within his family. One of his successors revolted against Roman rule anyway, but was unsuccessful.

Shipley (2000). The Greek World After Alexander, 323-30 B.C.