A choice made by the people of the state, usually via the mechanism of an election or a referendum, has caused states and governements to dissolve.

The first, and most potent answer is the parting of Czechoslovakia into the Czech Republic and the Slovak Republic in 1993. This was done by means of an act of the elected parliament the previous year, and resulted in the dissolution of the state into two new sovereign states.

The second answer is more controversial. I would argue that a major change in the methods of government may also constitute a dissolution of the state. For example Germany in the early 1930's. A democratically elected government transforms the state into a dictatorship within several years. I think it's fair to say that Germany of the Weimar Rupublic is not the Germany of the Third Reich, though both were undoubtably Germany.

(Note: "Collapse" should be taken to mean a loss of complexity. "Dissolve" means an increase of complexity. My definitions don't make great sense, but I feel we need some)

The number one reason states collapse or peacefully dissolve and are added to other states, including military reasons is:

The inability to adapt and react to change, or more commonly known as Gross Ineptitude, Mismanagement and Political Corruption

There are many theories concerning how and why this occurs.

First the WHY

This is not the best source, I apologize, but the conclusions we can draw from it will be pretty much the same.

The British historian Arnold J. Toynbee, in his 12-volume magnum opus A Study of History (1961), theorized that all civilizations pass through several distinct stages: genesis, growth, time of troubles, universal state, and disintegration. (Carroll Quigley would expand on this theory in his The Evolution of Civilizations.)

Toynbee argues that the breakdown of civilizations is not caused by loss of control over the environment, over the human environment, or attacks from outside. Rather, societies that develop great expertise in problem solving become incapable of solving new problems by overdeveloping their structures for solving old ones

According to Toynbee, the minority of people in a society who are problem solvers become entrenched and begin reflecting backward on their accomplishments, rather than working on solving the new problems. This dynamic results in internal conflict within the society until they are overthrown or the state collapses due to their mismanagement for some other reason.

Here's the HOW

Fragility of Complex Systems

As states become more complex, they have more points of potential weakness that could lead to a cascade of societal collapse. This explanation was commonly invoked to explain the recent global financial crisis. The Soviet Union is a possible example.

Limits of Imperial Conquests

As the title implies, many states that are empires will collapse or dissolve into other states when they can no longer expand their empire. Their entire structure of government is built around buying fealty of the military through the pillage of neighboring states. The Vikings and Mongols are examples.

Resource Depletion

Natural resources can be depleted if the leadership of a civilization do not take steps to adapt and create new ways of building homes, growing/raising food and trading with neighbors. An example is the Inca.

Occasionally, some states dissolve for other reasons, which likely they could not have helped:

Epidemic disease

The American Indians which encountered the Spanish for example.

Natural Disasters

Volcanic eruption, tsunami, mass unavoidable crop failures

Update - I forgot one of the most significant dissolutions by voluntary decision of the citizens. The Articles of Confederation were replaced by the United States of America after a plebiscite.

Don't forget voluntary incorporation. Texas decided to dissolve the Republic of Texas and join the United States.

Texas became an independent nation, the Republic of Texas. Attracted by the rich lands for cotton plantations and ranching, tens of thousands of immigrants arrived from the U.S. and from Germany as well. In 1845, Texas joined the United States, becoming the 28th state. The History of Texas

Sometimes a nation decides that they don't want to go it alone; sometimes a nation decides that joining a Union is a prudent choice, even if military force isn't a threat. Rhode Island joined the United States under threat.

Finally, Rhode Island, which had rejected the Constitution in March 1788 by popular referendum, called a ratifying convention in 1790 as specified by the Constitutional Convention. Faced with threatened treatment as a foreign government, it ratified the Constitution by the narrowest margin (two votes) on May 29, 1790. The Ratification of the Constitution

Climate Change and Natural Disasters

A strong factor in the dissolution of states, which can be observed all across history, is environmental change and disasters.

A few caveats:

1. I can't think of any examples in which environmental factors have brought about the direct and extremely rapid demise of a state (although local polities have certainly been annihilated by sudden and extremely violent environmental disasters, e.g. Herculaneum and Pompeii were famously wiped-out by the eruption of Mount Vesuvius in 79AD), as their role tends to feed into historical dynamics in subtle and complicated ways.

   This means that environmental accounts of historical change rarely have direct or immediate impact in the same way that military activity might. Whereas a sovereign territory could be invaded, its cities razed and its governmental and administrative structures dissolved inside of a month, in which case military activity is the obvious explanation of events, the effects of environmental change and disasters will not be so directly apparent when considered in relation to geographical constructs the size of empires and nations. Instead, it is more likely that the effects of slow-burning environmental change will accumulate until a tipping-point is reached, at which the prevalent arrangements of a state-entity may no longer be economically tenable. This may manifest itself as political and social unrest, migration, or even military annexation of surrounding territories, all of which may bring about the end of a state's political or administrative existence, but it has rarely (ever?) been the case that "environmental disaster X occurred, the Empire of Y collapsed as a direct consequence."

2. Closely related to the fact that environmental factors rarely have direct consequences is that these factors are rarely immediate. Here I note that your question related to state-entities "dissolving", the definition of which I take to include the relatively slow demise of a state. This could include scenarios of "deaths by a thousand needles", as well as the gradual detriment of a state's economic viability, leading to a consequent reduction in military clout. Similarly to my first point, it has perhaps never been the case that on day 1 there was state X, environmental catastrophe Y occurred on day 2, and on day 3 X was no longer extant.

3. While you're asking for historical reasons for the dissolution of states distinct from military action, I'd argue that military action has often been driven by other factors, and one such factor could be environmental change. Such is the glorious flux of history — change can seldom be taxonomised, and designations such as 'military', 'political', 'economic' are rarely satisfactory summaries of change. Humanity is complex; likewise are its motivations.

I've hopefully done a reasonable job of explaining that, so now for some examples:

The Bronze Age Collapse

It has been speculated that environmental change was a driver behind the massive migration that took place during the Bronze Age Collapse, an upheaval in population movements that has in turn been advanced as a cause of the widespread violence and destruction that saw a great many established states disappear from the historical record (indeed it seems that the historical record itself disappeared, a potent indicator of the collapse of civilisation).

The Bronze Age Collapse is a massive and complicated phenomenon ('event' doesn't really seem to be an appropriate designator), with myriad forces at play in its unfolding, but environmental factors which, it is speculated, have been influential include famine in Anatolia, drought and natural disasters.

The decline of Roman agrarian holdings

There is a thread of historical enquiry arguing that the relative decline in quality of Roman farming and pastural territory had a role to play in the gradual weakening of the empire, particularly in the Byzantine periods. The hypothesis runs that in the empire's north African territories and, I believe, in Syria, either climate change or over-farming, or perhaps both, actually caused the desert to extend into what had previously been productive agricultural land. The 'bread basket' was being devoured by the desert. This was detrimental in two ways:

1. Land that had previously been on the borders of the desert, and had thus been cultivatable, was now desert, and land that had previously been behind that frontier now was the frontier, and was thus of a lower quality. There was therefore less land from farming and pasture.
2. These 'frontier' regions had previously served as a useful buffer between desert peoples and the agrarian heartlands of the empire. As the desert encroached into these agriculturally-productive territories, so did the reach of those who dwelled within it, leaving imperial territory more exposed to raids, thus rendering its borders less secure and its soldiers far busier, and also reducing the productive capacities of the farmlands that would play host to such raids and skirmishes.

Please note: I do not have a nice source providing a summary of this process and an insight into its relative weight in comparison to other causes of the Roman and Byzantine Empire's (long) decline. If anybody could provide some useful links, I'd be very grateful!

The Maya Collapse

This is not an area of history that I know anything about, but so far as I understand things, many of the theories explaining the mysterious and dramatic collapse of the Mayan empire centre around changes in climate, soil exhaustion and drought. Indeed, similar reasons have been posited for the dissolution of other previously concentrated societies in South America, for example the Lambayeque.

Addendum

For me personally, environment (i.e. material context) is the bedrock of all macroscopic history, and humanity's shifting relationship with that environment, via the means of technology, is the locus of change. While many may not share my Marxist theoretical leanings, it is difficult to argue against the relative importance of environmental change and disasters as an agent for historical change, and included are the rise and fall of states. After all, there can be no society when there is nothing to eat.