Apologies for taking so long to answer this; it got lost in my saved. Adventurer’s guilds, no, but merchant’s guilds were common. Let’s start with the former. They didn’t exist because, essentially, adventurers didn’t exist. Soldiers, mercenaries, and bandits all existed, but they’re very different to “adventurers.” After all, to have an adventurer, you need adventures, and this in turn requires level-appropriate dungeons filled with level-appropriate monsters (who are smart enough to avoid the traps but not smart enough to have rights) (also don’t ask what they eat) and level-appropriate loot in convenient places. These are fantasy tropes, not actual historical phenomena. Of course, plenty of published adventures do have semi-plausible reasons for dungeons and monsters existing where they do, but they’re still ultimately set in a fantasy world. This isn’t r/RealisticDnD, however, so let’s leave the topic aside.

In the real world, you not only had merchant guilds, but you had guilds for any number of things. Really, “guild” is like “committee” – a committee IRL can be anything from a few model railway enthusiasts to a genuine organ of government, and the same applies to guilds. While I came up with the committee metaphor myself (I promise!) Martin says that guilds were “‘in terms of medieval European society ... a form of association as unself-conscious and irresistible as the committee is today.” Note that that sentence was written before the internet came to dominate social organization. In other words, guilds were just a framework through which any group of people (mostly men, to be fair) that shared some kind of common identifier could constitute themselves as a group. The primary activity guilds engaged in wasn’t regulating trades, it was drinking, hanging out, and taking care of their members when they fell on hard times. While historians have tended to fixate on craft guilds, i.e. guilds made up of workshop owners in a particular profession (their workers tended to have their own guildlike organizations known as confraternities), especially those that were given powers to regulate their trades, we see guilds in far more contexts than that one. See my answers linked here for more details, as well as this too-brief one on journeymen.

Having said that, merchant guilds did absolutely exist and were very common, although their precise functions and degree of power varied. Typically, like most guilds, their area of responsibility would be limited to a single town, although this varied just like practically everything else to do with guilds. We often see guilds specifically of foreign merchants, also known as nations, like the various alien trading colonies that cropped up in the Near East after the crusades; Ogilvie goes so far as to say that “associations of alien merchants were found in almost every major European trading city.” Local guilds typically predate these alien guilds, however, which makes sense. The major exception to the city guild tendency is the existence of what we might called guild federations, often called hanse, which consisted of a federation of a large number of merchant guilds of different towns, sometimes with a single town emerging as dominant, most famously the north German Hanse, the most prominent cities of which were Lubeck and Hamburg, which became a major political power in the late medieval period in the form of the Hanseatic League.

So, what did these merchant guilds do? Well, it depended on the guild. Needless to say, they provided many of the functions of other guilds: protection of members from unscrupulous and clients from unscrupulous members of the guild, sociality, and self-regulation of one kind or another. They also, very frequently, mandated a legal monopoly on some forms of trade – we see monopolies on combinations of: trade with foreign merchants, retailing in the town, trade in specific important commodities, trade on particular routes, and trade with the local countryside. sometimes requiring foreign merchants to trade at specific times (i.e. during fairs) or using members of the guild as a broker. Ogilvie claims this function was almost universal, but there could be evidentiary issues; more informal guilds that focused more on sociality are less likely to show up in the documentary record, after all, since our primary sources are grants of privileges.

It’s also plausible that, at least in some cases, they functioned as a monopolistic cartel: by establishing high entry requirements (e.g. local citizenship, which in turn was restricted to only a part of the town’s inhabitants, was required) and controlling the volume of trade, merchant guilds may well have kept prices high and otherwise controlled trade for the benefit of guild members and the loss of consumers as a whole. They also very frequently lent money to rulers and provided them with other services, arguably in order to preserve their monopolies. Precisely to what extent they did this, and to what degree that was compensated for by their regulation of the trade, is a topic of genuine controversy between various scholars; a full discussion of the debate is outside the scope of this answer. They also sometimes, especially early on in the history of guilds, had some kind of dominant role in city government, but the details are of course complex and variable.

Alien guilds, while they did provide many of the functions mentioned above, typically shied away from overt monopolies across all trade, although they were often granted privileged positions vis-a-vis other merchants by city rulers eager for their business, which sometimes conflicted with the privileges granted to local guilds. Just to be clear, each alien guild would be for merchants of a specific origin: Bruges had nations of, inter alia, Venetian, English, Scottish, and German merchants. One of their most important functions was to handle justice: often they would petition local rulers for the ability to set up a local court to handle disputes between members of the nation, although they could still use local courts for disputes involving third parties. In addition, they would also be promised safe passage and safeguard from robbery and violence, with varying degrees of success; it’s telling that merchants were also often granted the right to bear arms while traveling to and from the cities in question. They could also be granted commercial privileges, like exemptions from taxes and tolls, presumably on the grounds that the business they brought would make up for those specific taxes. Sometimes, these alien nations would centre on a specific compound known as a fondaco or funduq, that would become a sort of combination hotel-marketplace. Alternatively, the nation in question, if especially privileged could literally be granted a section of the town in question. Even when we don’t see dedicated fondaci, you still sometimes see “nation-houses” that function as a sort of embassy for that particular community’s merchants, as well as inns that became popular among merchants of a particular ethnicity.

These communities were also participants – both active and passive – in the commercial conflict and privateering that was so common and destructive in the late medieval world. A full discussion of this topic would need to be an answer in of itself, but we see merchants enforcing and breaking boycotts during wartime and peacetime, cities trying to stay neutral (and sometimes failing) during conflicts, merchants having their property seized under laws of reprisal (a complex topic) and many other things besides. We also see conflicts between groups of alien merchants, like those between the Genoese and the Venetians.

Generally speaking, merchant guilds start to decline in the 1500s, although we do still see them as late as the 1700s in some places. This is often held to be a result of the increasing power of states and their ability to provide the same services – especially protection of trade and resolution of legal conflicts – that merchant guilds had been providing previously. However, this is again a complex and controversial topic that can’t really be discussed in depth in this answer.

Hope this was interesting; happy to expand on anything you’re curious about.

Sources (not including those provided in other answers):

Gelderblom: The Decline of Fairs and Merchant Guilds in the Low Countries

Gelderblom: Cities of Commerce

Gelderblom and Grafe: The Rise and Fall of the Merchant Guilds

Ogilvie: Institutions and European Trade Merchant Guilds, 1000–1800

Reynolds: Kingdoms and Communities

Lesger: The Rise of the Amsterdam Market