One thing that has been highlighted about these “upheavals” is that their occurrence was not coincidental – although their exact causes have been and are being debated. This is reflected in various terms used in current research, including “age of revolutions”, “converging revolutions” or “world crisis”. I'll focus mostly on positions by Christopher Bayly and Armitage & Subrahmanyam to trace different influences on these developments. It's more of a starting-point going up to ca. the 1840s,without going into much detail on each case, due to the large time frame and complexity.

To give a brief overview, Bayly says that:

During the years 1756-63, warfare in the Americas and Aisa between Europeans and indigenous peoples, hastened the crisis of the old regimes in Europe. It helped to crack the financial systems of the old regime and throw doubt on the capacity and, ultimately, legitimacy of its rulers. The after-shocks of the subsequent European revolutions deepened the crisis of the old order in the Americas, Asia, and North Africa. But the cycle did not stop there. In turn, the repercussions of these extra-Eruopean conflicts fed back into the European convulsions.

He sees a turning point from the ancien regimes to new orders with the European revolutions, which had strong effects on non-European regions. By drawing on the concept of human rights, as e.g. put forth by Tom Paine, Asians, Africans and South Americans started opposition to any European “civilizing missions”. However, such doctrines were received in regiosn with their own histories of ideological conflicts, and adapted accordingly. One main factor here were the tensions suffered by the great agrarian empires', including the Asian ones.

Opposing forces to these empires could draw on European universalistic ideas for their challegnes of authorities. The new aggressiveness of the European states spread revolutionary ideologies across the globe, e.g. through the European colonial expansion in Asian and African states. Another example would be the major importance of Napoleon's temporarily taking over Spain on the Latin American revolutions of the early 19th c. These events in turn accelerated the emergence of modern nation-states and of what Bayly calls “polite, industrious and commercial societies.”

Bayly's quite detailed analysis highlights various influences on this earlier phase of world revolutions (late 18th – early 19th cs.). These include the globally rising costs of war, esp. in the Muslim empires and the Chinese empire, in connection with the silver influx from Spanish America; the increasing military expansion of European states following the French Revolution – both revolutionary and reactionary; and poverty and social conflicts leading to the questioning of the rulers' rights to rule more generally. For this latter point, popular culture and beliefs accelerated political and social conflict on an unprecedented scale, including a surge in apocalyptic movements (e.g. in China). Such developments in turn led to “ruling groups [reconstituting] the ideological foundations of the state and partially to modernize it”.

All this meant that (European) states could acutally benefit from the revolutions' influences in order to further centralize power, and to focus stronger than before on land rights in the colonies. In this way “the revolutionary wars [..] began to galvanize the fluid patriotisms of the 18th c. into the harsher lineaments of the modern nation-state”, but also influencing indigenous national identities. As a more general tendency, Bayly remarks a speeding up of two “modernizing” processes, the growth of uniformity between societies and the growth of complexity within them. These parallelisms can be seen as another way of answering your question, in that global exchange of goods but also ideas increased dramatically. .

Turning to Armitage & Subrahmanyam: They initially question the validity of the concept of “revolution” for such disparate developments, seeing how revolutionary promises were often only partially fulfilled. They also highlight different positions regarding whether long-term political outcomes of the Age of Revolutions related to economic/technological changes, whether these changes were relatively autonomous, or whether cultural factors were of greater importance.

More generally, it is mentioned that “the dimensions even of political change in the period under study were markedly heterogenous. In some parts of the world, formal political structures came crashing down, often without much shedding of blood and significant displacement of people […], while in others the same state-actors or their direct descendants remained firmly in place”. This stability in face of the revolutionary changes is underlined in certrain parts of the world – the Ottoman Empire being one example of this, in part due to a refusal to consider a kingless state. This shows how “even in 1840[...], the central political proposition of the American and French Revolutions – namely the replacement of monarchical government with some other 'popular' form – remained broadly unacceptable in the greater part of the world".

This seems to me an important addition the Bayly's focus on global change and influence: Not in all regions were revolutionary ideas adopted, or only some ideas that were acceptable to the regional conditions, and certainly were they not adopted in the same ways. Thus the authors ask whether “the flow of causal reasoning from Europe to the overseas territories might not at times be usefully reversed” (a point shared by Bayly and others).

What is more, for Armitage & Subrahmanyam influences were also exchanges between post-revolutionary societies and other forms of societies, including agrarian empires. Looking ahead they argue that “the decades from 1840 to the early 20th c. saw very few successful revolutions”, and that the revolutionary tradition was rather reinvented after 1900 – challenging a perceived continuity between revolutions such as the French and the Russian ones.

To sum up: It's not simply a coincidence, but finding the origins of these different revolutions, rebellions etc. is difficult. Various reasons have been raised to understand a "confluence of revolutions" in this time-frame: Including economical, military, and cultural ones. The spread of revolutionary ideals from the European revolutions and the (North) American revolution to other parts of the world has traditionally been seen as a starting point. It's important to stress here that this period coincides with an increase in European over-seas colonisation together with the beginning of an early industrialism (or "industrious revolutions"), influencing such parallel developments -- although 'Western' domination is usually said to have been further consolidated rather during the 2nd half of the 19th century. While the order of the ancien regimes in Europe was slowly starting to be undermined by revolutionary ideals, we can also see the beginning of a transformation from fluid patriotic sentiments to nation-states. The upcoming middle-classes played a stronger role in raising an ideological fundament for universalistic ideas and ideals. Bayly also underlines how European revolutionary ideals were on the one hand brought into regional contexts with their own conflicts; and on the other hand adapted by indigenous intellectuals and revolutionaries.

Armitage & Subrahmanyam add some important relativisations to these tendencies: On the one hand not all revolutions were by all means similiar in aspirations or outcomes. On the other hand in many regions revolutionary change was strongly resisted or led to a "hardening" of contrary tendencies.

As I noted this is all quite general, as I'm not equipped to go into all the examples you listed -- hopefully others can add to it. For a start here's an earlier answer of mine looking at global influences on the Spanish American revolutionary wars (with a focus on Bolívar).

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Sources:

• C.A. Bayly: The Birth Of Modern World 1780 1914. Global Connections And Comparisons (esp. Ch. 3, "Converging Revolutions, 1780-1820").

• David Armitage & Sanjay Subrahmanyam: Introduction, in ibid (eds.), The Age of Revolutions in Global Context, c. 1760-1840.

Edit: Formatting, summary

Follow up question:

What is the normal number of revolutions per century?

But were there actually more revolutions during that time period?

This seems likely to suffer from confirmation bias, as it could well be possible that there were just as many revolutions in other periods.

So, 2 quick points, on top of the great answer from /u/drylaw:

The first one is that Richard Evans has a book that just came out for the holiday season called The Pursuit of Power: Europe 1815 - 1914. It's part of the Penguin History of Europe series. Even though it's focused on Europe it has a lot to do with your question. After the Napoleonic wars the economy of Europe was in tatters, there were huge population losses (Evans even says that some demographers compare it to WWI when you take into account starting populations.) Balances of power were upset. For instance Napoleon's foray into Egypt embarrassed and weakened the Ottomans opening them up to British interference. Spain was no longer able to project power into its colonies in the New World and you had a bunch of people who had just finished the Napoleonic wars and were looking for a new adventure, like Admiral Cochrane. So I would highly recommend his book b/c it does have a lot of directly relevant information.

The second thing is VOLCANOES! (I'll be making my /r/badhistory premiere shortly) I'm only sort of joking. There were two big eruptions and a bunch of smaller ones during this time that impacted weather during an already cooler than average period. Along with everything else that was going on the eruptions created added strain on food availabilty. Mount Tambora is the most famous and responsible for the "Year without summer" in 1815. And just before that was a mystery eruption that probably happened somewhere west of Colombia in 1808. 1816 had crop yields that were as low as 25% of normal. This led to famines which played a part in social unrest like the Hep Hep Riots. So, while I'm not saying angry volcano gods caused anything above, a few very large eruptions played a part in altering normal weather, which impacted agriculture, which impacted food security and probably played some part on the political turbulence of the times. There's a neat book on the Tambora eruption titled Tambora: The Eruption that Changed the World. I can't recommend anything on the other mystery eruption near Columbia b/c I think it's just starting to get studied.

Hmmm. Can you say for certain that the number of revolutions from the mid 18th to mid 19th centuries was out of the ordinary?

Geoffrey Parker's seems to argue that it was the 17th century that was the period of revolutionary events. his article "Crisis and Catastrophe: The Global Crisis of the Seventeenth Century Reconsidered" counts 22 regime changes (the boldface events on page 1055, or in [this PDF] (http://www2.warwick.ac.uk/fac/arts/history/ghcc/event/events/parkerahr2008.pdf) it's page 4). the argument here is, the Little Ice Age happened in that century, and its adverse effects on agriculture destabilized nonindustrialized societies, rippling through politically and economically: http://news.nationalgeographic.com/news/2011/10/111003-science-climate-change-little-ice-age/ (edit: as u/elmonoenano has already pointed out, ash-&-sulfur-spewing volcanoes are thought to be a cause of the Little Ice Age)

EDIT: Historians have recognized this period as early as Trevor-Roper's 1959 book "The General Crisis of the Seventeenth Century". But more recently in 2013, Parker came out with an 874-page doorstopper that counted "fifty or so" rebellions in this period.

PS: from Parker 2008:

Because the mid-seventeenth century presented his reluctant reader with special problems of ennui, Voltaire decided to render the apparent anarchy intelligible by setting individual episodes within aglobal framework: "a period of usurpations almost from one end of the world to the other" that included Oliver Cromwell in Europe, Aurangzeb in India, and Li Zicheng in China.33 No doubt fearing that his 800-page metanarrative might exhaust Mme. du Chatelet, Voltaire ended his Essay in telegraphic style: "Three things exercise a constant influence over the minds of men: climate, government, and religion." Only this trinity, he asserted, could "explain the enigma of this world."34

At a very simple level there is always the possibility that the cyclical nature of stable states and unstable states undergoing upheaval hit a point in which there was a coincidental alignment in the timing of the unstable period across multiple states. Just to be the devil's advocate.