the revolutions can be seen as the product of inevitable intellectual and moral progression. The 18th Century had seen the popularization of science; a trend for fashionable monarchs (like Catherine of Russia!) to fund and keep close the most promising philosophers. Paris in particular developing "café culture" for discussing new ideas to be a social event. Travel around the globe brought new books written about different kinds of people - introducing the idea of cultural relativism. Chambers, amongst a sea of new publications, developed the first encyclopedia under the royal patronage of George II. Humanity was stretching it's wings - it needed a living exploration of the present mind of the nation. For years, knowledge from all over flooded in, becoming a communal project (and despite being banned by the church on occasion, was eventually completed).
It is said that this period was the final phase of Europe's old order - still largely agrarian, dominated by kings and landed aristocrats, and grounded in privileges for nobles, clergy, towns, and provinces continuing from medieval times. Yet Europe was still restricted by church dogma - and as Voltaire tells us, being "modern" depended on new ideas of independent reasoning, not religious doctrine, as the source knowledge. Reason and modesty, he said, will advance reality much more than ignorance and superstition.
In France, weak Louis XV was charmed by the beautiful and savvy Madame de Pompadour, who gained both wealth and power - often making important government decisions. The loss of the Seven Years' War (1756-1763 anglo-french, in locations all over the globe) accompanied by burdensome taxes, an ever-mounting public debt, more hungry people, and a court life at Versailles that remained frivolous and carefree caused even Louis to recognise a growing disgust in the monarchy.
Britain was recovering from it's own revolution at the beginning of the century (as Caddius touched on), having prevented absolutism without clearly inaugurating constitutional monarchy. The new political system was characterized by sharing power between king and parliament (1707 is when the English and Scots are united under the United Kingdom of Great Britain
). With the new parliament and first prime minister came a renewed value on liberty - a concept not new, traced back to the establishing of the Magna Carta in 1215.
Unlike the British, who gradually developed a system of public-supported poor relief, the French responded to general poverty with... not much. The king showed little interest in altering the serfdom system and the vast economic/cultural/social gap between nobles and peasants. Violence was contrary to human reason, but since so many philosophical ideas attacked any form of established order and authority, a revolutionary mentality was not out of the question for a large percentage of the population. 18th century philosophical propaganda, arguably, taught the Frenchman and the British colonists, like the American, to find his condition wretched, unjust and illogical.
So after the Seven Years war, Great Britain had become the world's *greatest* Colonial Power. Though, as mentioned, it sought to obtain revenues from it's colonies to pay for the expenses. The Americans, however, had come to believe that a king had no right to interfere with their internal affairs. The declaration of independence reaffirmed the Enlightenment's ideas of "natural rights" in the form of "life, liberty and the pursuit of happiness" "absolved from all allegiance to the British crown". And... fortunately for America, Britain had made a bunch of enemies durings the previous wars who were only too happy to help out!
So the American Revolution. Which became a profound example to all European observers, whose aristocrats wrote hundreds of books and analyzed lectures on how American independence had fired the imagination of those who were unsure of their status while at the same time giving the promise of ever greater equality to the common man."Everything must be shaken up, everything examined" said Diderot. Essentially, the idea that a better world was possible when created by men using reason.
Britain and France were largely intellectually on the same page after this, for a while. Until.... until France went over the top in following America's example. Using Rousseau's "by the people, for the people" mantra, peasants rose up... much chaos, death and destruction....
And then the British (like Burke) were like, oh, that's a bit unseemly. None of that for us thanks 
(Plus we love our queen too much
)