Uh, so this is a little more difficult than I think you realize lol. The issue is that the older, generally outdated, method of translating collegium is to say "guild." You'll frequently see that in older translations into English, but it's thoroughly inappropriate. Broadly speaking the answer to this question is a resounding "no." Certainly the closest thing to the medieval guild in the Roman world was the professional collegium, but it is decidedly unlike the guilds of Italian cities in the Middle Ages. Collegia were a type of voluntary citizen (or not, as most collegia allowed non-citizens and even slaves to join) association that is hard to classify according to modern analogs. The most general definition of a collegium is that it consisted of a group of people who met for some established purpose. The most important--and best-attested--forms of collegia were the religious and professional associations. The members of certain religious cults might collect as a collegium, as the famous worshippers of Diana and Antinous did at Lanuvium. These religious collegia probably had their basis in the priestly collegia, which immediately complicates viewing these associations as "guilds," as these priestly collegia were essentially classes of official magistracies. Likewise, members of the same profession in an area might decide to meet regularly as a collegium.

These collegia are the closest thing to a professional guild in the Roman world, but there are certain problems here. The first is that these categories are not necessarily very strict. Collegia often overlapped in their declared purposes, or did not really care much about them. The collegium of the lanii piscinenses ("butchers of the public fish-pond") in the Republic are known from a dedicatory inscription to the goddess Fors Fortuna. While they were a professional collegium they nevertheless exhibited a religious nature. Likewise we know of a collegium of dendrophori, the bearers of Magna Mater's ritual implements--are they to be considered a religious collegium by virtue of their cultic nature, or are they to be classified according to their shared profession? And collegia with avowed religious purposes were not necessarily so in practice. The foundational lex of the collegium of the worshippers of Diana and Antinous at Lanuvium survives, the only surviving collegiate lex in existence. The lex formally establishes the collegium as a religious one in service of Diana and Antinous, and then proceeds to ignore that provision almost entirely. Instead, the lex talks about the duties paid by members, the funerals that these duties funded, and the communal feasts that the collegium held monthly.

This last is the second part of our problem. While medieval guilds were collections of professional workers and often had a decidedly professional aspect (maintaining prices, etc.) the collegia of the Roman world were, as far as we can tell, purely social. We know of no professional collegia that involved themselves in the private business of their members or tried to exercise any sort of economic influence through regulation. The purpose of collegia was to act as social associations, first and foremost. They provided communal meals, a place for likeminded people to gather and converse, funerals (for some collegia), etc. In fact, this social aspect has led to a lot of problems with modern scholarship. In addition to the classes of collegia that I have already mentioned a couple of others are also proposed. Mommsen proposed three other types of collegia: collegia compitalicia, collegia funeraticia, and collegia tenuiorum (a broader class to which the first two belonged). Mommsen believed these (and a class of collegia sodalicia, "collegia of 'comrades,'" the existence and nature of which is the subject of enormous debate) constituted collegia without avowed religious or professional purposes, but which existed solely for the stated purpose of either political or social action. Increasingly it has become clear that these don't exist. There is a single attestation to a collegium compitalicium, on a late imperial inscription that does not elaborate on the term--in an article published a few decades ago Flambard suggested (although some still dispute it, I think wrongly) that this probably refers to professional collegia involved in the celebration of the Ludi Compitalii, not a separate class of collegia in and of themselves. There exists no evidence for collegia funeraticia (collegia whose purpose was to provide their members with funerals), a term which Mommsen invented--a recent monograph by Bendlin demonstrates that the Lanuvium inscription already mentioned, on which Mommsen based his conjecture, provides zero evidence that this collegium was of any "funerary" type whatsoever. This same monograph proves pretty conclusively that no broad class of collegia tenuiorum ("collegia of people of rather modest means") existed and that the senate of the Principate never issued the blanket order authorizing such organizations that Mommsen believed they did.

Certainly, though, these organizations were politically powerful. Collegia were highly organized, with elected magistrates and established hierarchies. The Commentariolum Petitionis points out the importance of courting such associations during elections, as their ability to vote as an entire block was crucial to securing the votes of the plebs media, the sort of professionals that were included in most collegia (as opposed to the unskilled day workers that made up the vast majority of the city's population). Historically a lot of scholars have supposed that P. Clodius' gangs were basically collegia with political purposes, a view that has no textual evidence as far as I can tell but is still very popular for some reason. What precisely the place of the Roman collegium in society was is pretty hard to accurately determine. Generally speaking they only resemble medieval guilds rather superficially, although a very few guilds might have been descended from collegia, but what exactly they were is a little harder to say. The big issue here is that we're very starved for information. Our texts do not talk about collegia often and when they do it's in almost no detail. Epigraphy is a helpful tool, but collegiate inscriptions are dominated by particular types of collegia and generally only include particular types of inscriptions, which causes a problem in the selection of our material.

May I tag another question with this one? Was the schools of philosophy equivalent to guilds as in the medieval periods?