An associated state is the minor partner in a formal, free relationship between a political territory with a degree of statehood and a (usually larger) nation, for which no other specific term, such as protectorate, is adopted. The details of such "free association" are contained in a Compact of Free Association or Associated Statehood Act and are specific to the countries involved.
All free associated states either are independent (with status of subject of international law) or have the potential right to independence.
Informally it can be considered more widely: from a post-colonial form of amical protection, or protectorate, to confederation of unequal members when the lesser partner(s) delegate to the major one (often the former colonial power) some authority normally exclusively retained by a self-governing state, often in such fields as defence and foreign relations, while often enjoying favorable economic terms such as market access.
A federacy, a type of government where at least one of the subunits in an otherwise unitary state enjoys autonomy like a subunit within a federation, is similar to an associated state, with such subunit(s) having considerable independence in internal issues, except foreign affairs and defense. Yet in terms of international law it is a completely different situation because the subunits are not independent international entities and have no potential right to independence.
The Cook Islands (since 1965) and Niue (since 1974) - neither is independent - are formally said to be "in free association" with New Zealand. The residents of those islands are New Zealand citizens. In contrast to the US situation, those territories are not treated by the UN as independent states, although the Cook Islands have the right to declare independence, are parties to several international conventions (such as the convention on children's rights) and regional organizations, and already maintain diplomatic missions in other countries.
In early February 2006, Tokelau voted in a referendum to determine whether it wanted to remain a New Zealand territory or become the third state in free association with New Zealand. While a majority of voters chose free association, the vote did not meet the two-thirds threshold needed for approval. A repeat referendum under United Nations supervision yielded similar results in October 2007. 
The Commonwealth of the Philippines was the first associated state of the United States. From 1935-1946, the foreign affairs and military of the commonwealth were handled by the United States although it was otherwise constitutionally separate and independent in domestic matters.
The Federated States of Micronesia (since 1986), the Marshall Islands (since 1986), and Palau (since 1994), are associated with the United States under what is known as the Compact of Free Association, giving the states international sovereignty and ultimate control over their territory. However, the governments of those areas have agreed to allow the United States to provide defense, funding grants and access to US social services for citizens of these areas.
Puerto Rico (since 1952) and Northern Mariana Islands (since 1986) are non-independent states freely (willingly) associated with the USA. The commonly used name in Spanish of the Commonwealth of Puerto Rico, Estado Libre Asociado de Puerto Rico, literally "Associated Free State of Puerto Rico", which sounds similar to "free association" particularly when loosely used in Spanish, is sometimes erroneously interpreted to mean that Puerto Rico's relationship with United States is based on a Compact of Free Association and at other times erroneously held to mean that Puerto Rico's relationship with United States is based on an Interstate compact. This is a constant source of ambiguity and confusion when trying to define, understand and explain Puerto Rico's political relationship with the United States.
For various reasons Puerto Rico's political status differs from that of the Pacific Islands that entered into a Compacts of Free Association with the United States. As sovereign states, these islands have full right to conduct their own foreign relations, while the Commonwealth of Puerto Rico has territorial status subject to United States congressional authority under the Constitution's Territory Clause, “to dispose of and make all needful Rules and Regulations respecting the Territory…belonging to the United States.”  . Puerto Rico does not have the right to unilaterally declare independence, and at the last referendum (1998) the narrow majority voted for "none of the above", which was a formally undefined alternative used by commonwealth supporters to express their desired for an "enhanced commonwealth" option. 
A formal association existed under the Associated Statehood Act 1967 between the United Kingdom and the six West Indies Associated States. These were former British colonies in the Caribbean: Antigua (1967-1981), Dominica (1967-1978), Grenada (1967-1974), Saint Christopher-Nevis-Anguilla (1967-1983), Saint Lucia (1967-1979), and Saint Vincent (1969-1979). Under this arrangement, each state had full control over its constitution. The United Nations never determined whether these associated states had achieved a full measure of self-government within the meaning of the United Nations Charter and General Assembly resolutions. Within a few years after the status of associated state was created, all six of the former associated states requested and were granted full independence, except for Anguilla within the former St. Kitts-Nevis-Anguilla, which separated from the associated state before independence and remains a United Kingdom dependent territory.
In a loose form of association, some of the foreign affairs of these three European nations are handled by the indicated countries. Otherwise, they are constitutionally separate and independent in all other matters:
Three Crown dependencies are in a form of association with the UK. They are independently administrated jurisdictions, although the British Government is solely responsible for defence and international representation. They do not have diplomatic recognition as independent states, but they are not part of the UK, nor do they form part of the European Union. None of the Crown dependencies has representatives in the UK Parliament. These are the Crown dependencies associated to England and later the UK:
The foreign affairs of Bhutan, a Himalayan Buddhist monarchy, were partially handled by the neighbouring republic India (since 1949), which thus in a sense succeeds its former colonizer Britain's role as protector, in a loose form of association, although Bhutan is otherwise constitutionally separate and independent in all other matters. Before its merger with India (1947-1975), a similar relationship existed with Sikkim, which is now a constitutive state.
This kind of relationship also can be found in the Kingdom of the Netherlands, where the continental part is organized like a unitary state but the status of its external territories - Aruba (since 1986) and the Netherlands Antilles (since 1954) - can be considered associated non-independent states. After the split-up of the Netherlands Antilles (on 15 December 2008), Curaçao and Saint Maarten will be associated states like Aruba. Although this relationship is similar, the Kingdom of the Netherlands is actually a federacy.
According to a law of the Republic of Tatarstan (1990-2000), and the Treaty of Mutual Delegation of Plenipotentiaries between it and the Russian Federation (1994), from 1994 to 2000 Tatarstan was considered a sovereign state under international law, but associated with Russia. But between 1994 and 2000 there was no international recognition of Tatarstan as an independent state.
According to statements of officials of Abkhazia and Transnistria (self-proclaimed unrecognized republics seceded from the meanwhile independent, former USSR's formerly constitutive Soviet Republics Georgia and Moldova), both intend after recognition of their independence Abkhazia and Transnistria to become associated states of the Russian Federation. In Transnistria a referendum took place in September 2006, in which secession from the Moldova and "future free association" with Russia was approved by a margin of 97%, even though the results of the referendum were internationally unrecognised.