First, I assume you are talking about Western Europe, where this sort of trope is most common. Secondly, the 14th century was a time of a lot of social change. The earlier half saw the separation of the estates near it's zenith, and the later half saw a great expansion of the power and freedom of the lower classes. The middle part was mostly dying. Third, depending on where in W. Europe you are curious about, the answer might vary quite a bit more than you expect. England, for example, had virtually no serfs by the 14th century, while the more Eastern reaches had far higher numbers. Some Germanic kingdoms didn't outlaw serfdom until the 1800's. Lastly, what is a peasant anyway? Does it encapsulate all farmers? Only the poorest farmers? Serfs and slaves? Just anyone of the lowest class including traders or merchants? It can be a really nebulous concept. Don't even get people started on terms like Feudalism.

A disclaimer, all of this must be painted with very broad strokes of the brush since there are so many possible permutations, but I think they will help you conceptualize the era better and perhaps refine your question. To be much more specific would require pages and pages of information for such a simple question.

First of all, take the image of the medieval Alehouse or Inn in your mind and throw it away. It probably never existed. Romantic poetry and writings have vastly over estimated how urban medieval Europe was, and only a real city would be able to support a full time brewer or innkeeper. The Inn or Brew-house you are imagining filled with bards and spitted pigs is probably an 18th century Coaching Inn projected backwards via the magic of imaginative writers. Even those would be pretty different. Anyway, assuming your town happens to be big enough to employ a person selling alcoholic drinks even part time, this person probably just does so out of their house. Inns would be pretty similar, just sharing a bed or room with the home owner, or sleeping on the ground. Perhaps a widow does it to generate some extra income. This itself is a bit of a stretch already, since most towns wouldn't have a dedicated alehouse or brewer. Plenty of people brewed their own beer to drink, it wasn't hard to make a small beer; though, I think they taste quite terrible. Drinks are likely to be served to you outside at a table or bar-like setup you stand at and yak about the weather. If their house is big enough to allow people in to sit by the fire it still feels like you are just sitting in their living room/bedroom on their stools or benches, because that is exactly what you are doing. That's assuming they trust you enough to let you inside.

So lets talk about payment. Assuming the brewer knows you, which is most likely since you both grew up in the same town of about 200-500 people, you may be able to skip out on the drink unnoticed. The person probably may not be paying a lot of attention to you since they know your reputation is on the line. Remember, this is assuming brewing isn't their primary source of income. Assuming they don't report you to the local sheriff (nobody likes trouble) they will probably come just come to your house later and ask you to make good on the bill at some point. If you refused still, they might show up again with some friends and family to make sure you see the error of your ways. They probably aren't breaking any kneecaps, violence is technically a monopoly of the nobility, they just want the whole town to see what a crappy person you are, and to pressure you socially. This was a pretty common extra-legal tactic for restitution prior to the 19th century. If you refused to pay your reputation would suffer in the town greatly. The vast majority of financial transactions prior to the 19th century would be performed without any currency. Most things were traded for goods or labor in kind. If you were a farmer you might pay with extra food you had or the promise of food later, if you were a laborer, you would promise to help them with work later. Most people just didn't have money to spend on anything they couldn't make themselves anyway. If you have no reputation, nobody will trust you to repay the drink with food or labor later. At this point they may or may not report you to the sheriff, who may or may not do anything depending on how much he cares or how busy he is. A sheriff's job is really to make sure taxes are flowing into the hands of the nobility and to keep an eye on things.

So what if you're in another town and try all this? Well, first off the brewer probably wouldn't let you in his house. In fact, how are you getting in the town at all? Reputations are very important, and unknown people are probably trouble. In all likelihood nobody will serve you much of anything if they don't know you. They might let you come in town during the day to do some business and trading, but you would be expected to leave at night and pay either immediately after receiving the drink in trade goods or money. A dedicated brewer or person running an innhouse is likely to be watch patrons like a hawk about payments, but that is another story. How did people move towns back then, you may ask? Rarely, and they probably knew someone in the town they were going to who would vouch for them. You would probably need the permission of the local lords to move in anyway. If the brewer doesn't know you he might not take labor in kind since he doesn't know your reputation, so he would want real money. Skipping the bill is possible for sure, but you would be most unwelcome there again, possibly a persona non-grata in the whole town. Finding a person you didn't know who had skipped town would be virtually impossible, especially for such a minor crime. This isn't even addressing the fact that most peasants, and especially serfs, might not be legally allowed to leave their land or the town the resided in, and even if they did they probably didn't have the means to get very far, much less purchase a drink.

At the end of the day, most peasants would make their own beer to drink, probably didn't have coins laying around, and probably couldn't or wouldn't leave their town. Real inns or alehouses would only exist in cities, and were probably patronized by people of a slightly higher class than peasant.

I hope that helps some.

Edit:

Sources: This is purposely written broadly, and so I am absolutely sure you can say X isn't true in place Y. Generally one would probably use The New Cambridge Medieval History Volume 6: c.1300–c.1415 as a source for general information on the Medieval world. I also drew on lots and lots of books and lectures on Medieval and Early Modern Germany, which I am most familiar with. When I get home I can dig up a few more titles, but off the top of my head Germany in the High Middle Ages by Fuhrmann, and German Home Towns by Sheehan, though it addresses a later time period, much of it is relevant regarding social norms. Same with Power in Blood: by Sabean, later time period, but interesting insights.

Other interesting work to consider: I have not read At Play in the Tavern: Signs, Coins, and Bodies in the Middle Ages, but it may provide some insight; though my understanding is that it is more about the perception of Taverns.

Housing the Stranger in the Mediterranean World: Lodging, Trade, and Travel in Late Antiquity and the Middle Ages would also be interesting, but seems to mostly deal with Greek and Latin culture, and only really to about the 12th century.

Other Threads of interest: https://www.reddit.com/r/AskHistorians/comments/1ecbg1/what_wrong_ideas_about_medieval_europe_might_one/c9z3z05

https://www.reddit.com/r/AskHistorians/comments/rjq1f/what_were_medieval_taverns_like/

https://www.reddit.com/r/AskHistorians/comments/1np7cu/are_there_first_hand_accounts_of_medieval/

https://www.reddit.com/r/AskHistorians/comments/3kkncv/were_medieval_inns_real_or_the_creation_of/

Is there a particular country that your interested in?

Historical background: English alehouses, specifically, undergo a transition in the later 14th century. Brewing ale was a fairly standard in-home chore--ale was part of the daily diet. At the beginning of this time frame, ale houses were most often literally "houses that sold ale." A family with another baby on the way or compensating for the loss of a valuable livestock animal would brew extra ale one week, put up some kind of sign outside to notify fellow villagers or townspeople of ale for sale, and hope they reeled in customers looking for a drink in good company. (Medieval ale had a very short shelf life.)

Towards the end of the century, alehouses start to become more permanent establishments alongside their wine-, food- and lodging-providing counterparts. I'm not personally familiar with a decisive argument for the shift, although the drop in grain prices around that time would have made mass-brewing of ale significantly more economically feasible and potentially profitable.

In the earlier part of the century, ale was sold as often for consumption off premises as in the alehouse, so we can safely assume payment before drinking in those cases. Additionally, if you were simply popping into your neighbor's house for a drink and a chat (or a knock-down, drag-out barfight!, cf. Bennett, 20) at the end of the day, it would be pretty hard to get out of paying one way or another.

With more permanent establishments--and here I'm going to broaden the scope to taverns and inns as well--court records can be ambiguous as to the order of service and payment, although it seems like payment came last. Ruth Karras has a couple examples of a "tavern guest" meeting up with an accused prostitute and her pimp:

"The ostler conveyed her to the George into a chamber there and after came the priest...they went to supper all three and the priest paid for all." (*Common Women, 72)

Payment for lodging and food after the fact seems to be supported by literary sources--in the 12th century French Erec et Enide, Erec pays the duplicitous host on his way out the door; the conniving tavern host-priest (...always a priest) in the fabliau Le prestre et le chevalier lays out a lavish meal to the knight's delight--then proceeds to charge him for each item down to individual flecks of pepper.

Indeed, these literary sources paint a pretty grim picture of the public reputation of hosts-for-profit--and alehouse keepers are no exception. If anything, the situation is worse: they're a frequent character in artistic depictions of hell, and two of the seven personified Deadly Sins in the English poem Piers Plowman are associated with brewing ale.

Which is to say, take the source record on alehouses for what it is: people dealing with a vital, omnipresent, but morally ambiguous aspect of their world, with all the biases that entails.

That said, when ale-sellers show up in court records (at least, for reasons unrelated to licensing), it's generally because of customers' accusations that the sellers cheated them on measurement. This probably reflects a combination of alewives as an easy target with the alehouses' roots as a house: your "cup" or "glass" of ale was probably any old container the owner had on hand, so standard measurement was a judgment call. Still, though, the general paucity of reverse accusations--sellers suing customers for lack of payment--suggests that brewers were pretty good at preventing people from skipping out on their payment. (Also, if people skipped their tabs, presumably they wouldn't be suing over dishonest measurements.)

One of the most well-known satires of ale sellers, John Skelton's The Tunning of Elynour Rumming, portrays an alewife who squeezes every last bit of payment out of her market. She chases away people who can't pay

With a 'Hay, dogge, hay! Have these hogges away!'

With 'Fo, ther a stench--Gather up, thou wenche

Take up dyrt and all

And bere out of the hall

collects payment in anything and everything that people can offer (even encouraging customers to go into debt):

Anone cometh another, as drye as the other,

And wyth her doth brynge mele, salte, or other thynge,

Her harvest gyrdle, her weddynge rynge

To pay for her scot as cometh to her lot

and, um, enriches her ale with a secret ingredient:

And somtyme she blennes the donge of her hennes

And the ale together; and sayeth, Gossyp, come hyther,

This ale shal be thycker and flowre the more quicker.

Obviously, or at least one hopes, that is satire, and your good neighbor wouldn't sell you chickenshit in exchange for your wedding ring. Although Elynour mostly comes out on top in the poem (which is very English--in contemporary German literature, transgressive women never win), the poem suggests that the people she's kicking out for lack of payment have already consumed at least some of her ale:

With, Get me a staffe--the swyne eate my draffe

Stryke the hogges with a clubbe,

They haue dronke vp my swyllynge tubbe

Again--it's satire. But if we take the usual way of interpreting satire as rooted in reality so as to seem realistic though exaggerated, at least some of the time, alehouse guests by the end of the Middle Ages were drinking up before paying up. This would reflect the norms already established by taverns and inns, back in the days when alehouses were transient neighborhood affairs.

~~

Sources: Judith Bennett, Ale, Beer and Brewsters in England, 1300-1600; Ruth Mazo Karras, Common Women: Prostitution and Sexuality in Medieval England; Andrew Cowell, At Play in the Tavern: Signs, Coins and Bodies in the Middle Ages; go read Elynour Rumming, it's fantastic

ETA: to credit Skelton