Hello! This my first answer in a looooong time so please be gentle as I try to shake off the rust!

So first thing first, as always, it depends. You acknowledged yourself that the scope of your question was very large and so I will focus on the time period and the place I know best : late XIV-early XVth century Burgundy (as is, lands of the Dukes of Burgundy, including in Flandres, Picardie, etc).

The main point to consider is the fact that the status of peasants evolved quite a lot during the medieval period, especially as servage was progressively phased out, a process nearly over at the end of the XIVth century in France. Not entirely over, but close.

Originally, serfs were not considered free men, yet their status was not that of a slave. A serf had a legal existence as a human being, he wasn't considered a mere tool or object, he could testify in justice and even make contracts, to a certain extent. He was, however, bound to a land, a parcel, that he had to cultivate for his lord. He owed his lord a number of services and in return he benefited from some protection. Military one, of course, but also "ownership" one : he could not be expelled from his parcel of land because they were considered to be two parts of the same thing. He couldn't be sold either, although his land could be bought or exchanged between lords and he would change lordship with it. He was also permitted to marry (with the accord of his lord), mainly among other serfs.

This status was progressively phased out and the Black Death of the middle of the XIVth centry, decimating the population, made the peasant a valuable ressource and thus accelerated the process. Keen to attract new people able to take care of their lands, lords started buying serfs "contracts" to their overlord, promising the peasants freedom and a plot to use freely. And the overlord, of course, could improve their serfs conditions to try and keep them.

A number of other factors were at play, of course, such as the multiplication of villefranches (ie : free-cities), were runaway serfs were out of reach of their overlord's droit de suite (ie : right to pursue) and other kind of refuges in which serfs were not to be pursued anymore.

The progressive disparition of serfs led to the rise of a free peasants class, that had already existed along serfs for quite a long time but became progressively the majority and of peasants. Those peasants were free men, working for themselves (in theory) or as employees for a landlord or another peasant. They had every right to sell their lands, to inherit form their parents, to marry whom they pleased or to sell their surplus.

Now, medieval society still relied on the principle of double ownership : simple ownership and éminente ownership. It is a bit like a landlord nowadays has to pay property taxes to the state. Your lands are part of a baronny, or a county, or a duchy, ... and so your lands also belong to your lord and you have to pay a fee, because in a way you're renting the land. I've elaborated a bit on this topic here.

Now the other thing that makes it complicated is local disparity. In a way, the answer to your question is "A LOT". As I've explained a bit in the previous link and here , rights and priviledges were very different from one place to another. On the other hand, your answer could be "very few", because the lords were not the only characters at play. Rights and priviledges were the result of negociations. The power of kings and lords during the middle ages tend to be exagerated by modern representations. In reality, they could rarely afford to be tyrannical overlords. Of course, you can deny any right to the cities you rule. But you better not need them to pay your ransom. Or to consent to taxes. Or to provide military assistance. Or to take part in their fortification effort.

As a rule of thumb, rights and priviledges were the product of negociations, sometimes very ancient. "This tax ? Oh, but my lord, it has been given by your grand-father in 1214. He needed to answer the call of the king and fight at Bouvines, and he was out of funds. We obliged and made sure he could ride with a hundred men-at-arms, and in exchange he gave us the product of this tax forever. Oh, you want to collect it for yourself now ? I'm sure we can reach an agreement!"

Of course those agreements were as local as it gets, every city, county, province - or anything really - could obtain specific rights. Those rights could regularly be confirmed by the lords and kings, at the request of their recipients, to make sure they were not forgotten or removed. The most famous one, the Charte aux Normands, was conceded by the king in March, 1315 and confirmed in july 1315, 1339, 1381, 1419 (by the king of England acting as king of France), 1423 (same), 1458, 1462, 1485, 1508, 1517, 1550 and 1579!

The extreme example of such local particularity can be found in the division between the two main justice systems of France. The southern part of France was following the motto of "Pas de seigneur sans terre" (no lord without land), meaning anyone having a claim as lord of a land had to make sure he had the adequate papers to prove it. It was an heirloom of the roman justice system and that made the terriers, aka the place were the lord kept such records, a prime target for rebellions and uprisings. The northern part of France was following the idea of "Pas de terre sans seigneur" (no land without a lord), meaning every plot of land was, in definitive, owned by a lord, and you could only claim specific rights or exemption by provinding the papers, thus reversing the burden of proof.

I hope that helped, feel free to add any follow-up question, although it might take some time for me to come back to this obviously!