Most role-playing games (and other popular depictions of European history, for that matter) ignore the nuances, and lump all peasants into a single social class just above criminals but below everything else. In most peoples' minds, peasants are illiterate, unwashed, and poor. They toil all day in the mud growing crops on small plots of land, live in cramped little shacks made of sticks and horse crap, have very little money, and are generally treated like crap by their superiors and often have to worry about armies marching through and stealing all their crops and livestock and murdering them for the lulz. These connotations survive to the present day with the use of the word "peasant" as an insult.
Oversimplification aside, this does reflect the truth to a degree at least. In the middle ages in Europe peasants were expected to give between 10% and 30% of their crops to their lords and 10% to the Church as tithe and the rest they either ate themselves or sold for a few pennies. As well as paying conventional taxes, they had to pay a corvee, a tax of days of work on various things such as working in the mines, repairing bridges, building cathedrals and so forth and generally had to follow the local lord's rules and his judgements. That said, the nobles had an obligation to defend their peasants by fighting and building castles for them to hide in when vikings came, as well as doling out rations if there was a major crop failure (after all, if your peasants were all killed/sold into slavery/starved to death they won't do your shit). They also had to hold feasts for them on important holidays (46 days a year in medieval England, how many feasts did you go to last year?) and protect their local interests. That said, how well these obligations were upheld varied a lot from lord to lord, there was plenty of room for corruption and the mechanisms to respond to abuses of power were crude at best and actively stacked against the peasants at worst. If an illiterate serf bound to the land gets the crap kicked out of him by his Lord because he looked at him the wrong way, there was not much he could do about it even if it the law stated that this was illegal.
In Medieval Europe peasants usually stayed out of warfare. Since agricultural work was where nobles got most of their income and in general feudalism was founded on the idea that nobles and knights protected peasants from all the bad people out there this made sense. That said, militarized peasants were employed at various times as defensive militiamen and "levies", peasants volunteers or conscripts given some training and weaponry used mainly as infantry and brought along on campaign to bolster the ranks before being sent home to bring in the harvest. Peasant Levies were considered as being the more disposable section of a medieval army, they lacked the discipline and resolve of well trained professional soldiers (historical note: the last truly professional full time soldiers in Western Europe before the modern age were the Romans) but they did not take a decade to train like a proper knight did. Doing this too much was generally bad for the economy as these guys would not be farming while they were off on campaign and especially if they were dead. This also limited the time in which wars could happen to those months when there was not farming to do. For these reasons European Peasant Levies steadily declined in use over the middle ages and were superseded by more professional common born soldiers who would be constantly under arms, though some of these guys were still drawn from the peasant classes. Even so, by the late middle ages gathering up a mess of peasants off the fields, giving them spears and old helmets, and using them as a major component of your army when not on the defensive was an act of desperation. After the middle ages, peasants were again used for military manpower for soldiers in centralized professionalized standing armies, though up until the the French Revolution and the Levee en Mass this was not much of an issue given that that a standing army would make up a fairly small percentage of the population.
Some role-playing games have adopted the less judgmental term of "commoner" for the class of "regular people", even though "commoner" technically refers to anyone in the middle ages who was not a noble be they poor peasant or prosperous merchant who is wealthier than many lesser noble houses and they aren't any better off -- in fact, a common cat is a serious threat to a level-one commoner.
This system began to falter after the Black Death, since with so many peasants dead the remainder suddenly became a valuable commodity, especially since cheaper land prices and better wages meant some peasants could elevate themselves to the nascent middle class. However, this did not occur in Eastern Europe, which was relatively unscathed and put in even harsher restrictions in the form of serfdom.
With the Industrial Revolution, one man with mechanical and chemical assistance could farm as much land as a hundred peasants, so there was no need for vast numbers of unskilled and semi-skilled laborers to support society, and the serf system (and feudalism in general) came to an end (at least in the West, it would hold on all the way into the late 1800s in places like Russia). Instead they were brought into the towns, women and children were set to work on dangerous machinery, and their population was kept artificially high to keep down wages. Thank god for James Watt and John McKormick.