Although I can speak only to the Holy Roman Empire (HRE, which roughly corresponds to today's German), I would say that peasant revolts were, during the later Middle Ages (14th to 16th century) significant.
Furthermore, you have to read the book I cite: Peter Blicke, trans. Thomas A. Brady Jr, "Obedient Germans? A Rebuttal (Deutsche Untertanen: Ein Widerspruch)", (Charlottesville, VA: University Press of Virginia, 1997). It is short, it is concise, and talks about precisely what you are talking about, with the specific lens, again, of the Holy Roman Empire.
First, what made these types of revolts possible? The term that you are using "peasant" was less commonly used than either "common man" or "subject" (in German: Untertan). The latter term was more frequently used, as it inherently expressed the relationship between a strong authoritative state and one who was ruled. Furthermore, there was not a complex societal divide: there were subjects, and there were nobles (and the clergy, who weren't the butt of many revolutions in the HRE, at least). One of the earliest terms of this divide is found in the Erfurt compilation of customary law of 1289 under the heading "Head Tax": "No one shall be exempt from the head tax, neither priest nor layman, neither noble or commoner". As you can see, there is an ideological division of society: nobles, and everyone else. This made it very easy for everyone else to feel solidarity and eventually revolt. (4-5)
Around 1300, Central Europe changed and produced "communes". These were "associative bodies [...] that both claimed by right and undertook to perform tasks of a political nature" (11). This changed the hierarchy from vertical to horizontal; associations were now made to the neighborhood, rather than just the lord. Again, a building of solidarity which would later help to provide rights. Also, peasants were able to command their own labor because they paid indirect rents to the landlord in cash and kind; the servile farmer was now a peasant in the stereotypical sense of the term (15). Finally, peasants were under the direct power of not only the lord, but the court, and the village mayor, as well as the watch, the last of which they elected. This seems to control the peasants more, but was in fact very freeing as they now had other forces to appeal to if their rights were being trampled.
Finally, riots. An important aspect of the riots is that they were "violent actions that did not go beyond a refusal to obey, and which thus contained no desire for innovation" (62). There were about 130 peasant revolts in the HRE between 1300 and 1800, even counting only those movements which involved several villages. Most occurred in the 7 or 8 decades following the Reformation. These revolts occurred in the south and southwest HRE from 1300-1525, and the areas most affected were Switzerland and Austria.
What is a peasant revolt? It had five fairly distinct stages:
It is also important to remember that in addition to peasant revolts, there were urban revolts (roughly 250 during the same centuries) which inherently involved more people and thus threatened the governmental system; in fact, those cities with the strongest governments were the most susceptible to revolts. (72).
For an example of a single, widespread peasant revolt in the HRE, look to the German Peasant's War.
In Sweden it ws extremely common during the later parts of the medieval era, from the Engelbrekt rising 1434 and onwards, peasant risings became such commonplace that the peasant militia, already decently well armoured and trained, became experienced and organised enough to be capable of defeating a force of Northern Europe's finest mercenaries and the personal guard of the Danish King entrenched with cannon atop a ridgeline at Brunkeberg 1471. Not promising to respect the old rights of the peasants AND actually doing it became a swift way to be dethroned during this era in Sweden.