"In a free society, what stops corporations from becoming monopolies?"
Or (and this was part of a rational, reasonable discussion, and certainly not a fallacy itself, so I only include it here as an example of the question, especially as the first response was directly to it):
"Just so I understand your position completely: Would you propose any sort of system to keep corporations in control, to limit monopolies and oligopolies? Or do you propose we only depend on the free market?" (Angela Roby)
Depend on the market. Depend on the distributed power of individuals to respond to force with force, or even things that are not force or fraud per se but "unfair practice" (racial discrimination, various acts called "exploitation", misleading advertising) with ostracism, or simply not buying from such companies if alternatives exist.
There are a few sorts of monopolies: those established by force (e.g., a city gives a cable provider a monopoly and stops anyone from competing), or fraud, or other criminal acts, and those established peacefully.
To give a simple example of a peaceful monopoly, consider the first coffee shop that opens in a town. It's not shutting anyone out, and it is likely that there will be competition if their is demand, but for now, it's the only place to buy coffee, just because it was first. Clearly it's doing no harm. If it overcharges for coffee, people can leave town to buy it (it only has a limited regional monopoly), brew their own, or compete with it.
Qualifying what the monopoly is in is important, too. If there is also a tea shop (that only serves tea) in town, the coffee shop has a monopoly on coffee, but not "hot beverages"... and then if there's a soda fountain or grocery store, they share a market for "beverages" in general. At the most basic, everyone has an absolute monopoly in their own labor. It will usually be part of a class of labor ("basketball player", "barista", "lawyer"—or "criminal lawyer"—or "torts lawyer specializing in mechanical sock-sorting patent infringement claims") but the point stands. Microsoft was adjudged to have had a monopoly on "Windows", but not operating systems in general.
Another form of peaceful monopoly is just a company that is better at satisfying its customers—there are no artificial barriers to competing, but people try and they can't be as efficient, or their recipes aren't as well-liked, or their pay scale makes their employees surly, whatever.
And again, in line with the "first in town" is the "first inventor". I've used an example of autonomous (self-driving) vehicles in the past. If Joe starts a business selling converted Corollas, charging, say, $22000 ($5k over the base $17k price, which goes to the extra effort to install the computer driving mechanics, profit, research, etc.), then he has a monopoly as first seller.
(Aside: no patents in a free society—there is no right to do harm to someone for copying your idea.)
Fred copies Joe's idea but uses an Aveo body which he can get for $15k and manages to reduce his costs to $4k, for a sale price of $19k. Joe cuts his overhead to $4k but is still at $21k; customers start flocking to Fred. Joe no longer has a monopoly on autonomous vehicles, but he does have one on autonomous Corollas.
Let's suppose that Joe makes a bundle on his business, and isn't investing much back into it; instead, he buys a private island and passes the business to his son, who's not so sharp. Meanwhile, Fred has employee profit-sharing plans (giving his employees incentive to work harder); he manages to cut his overhead to $3k; he invests in continuing research; and he adds Corollas and other body types to his lineup. Joe's former company goes out of business, and Fred's a monopoly now. But is it a license to print money? Heck no. Other people would be looking at competing, and if Fred doesn't stay on the ball—keeping customers happy—they'll swoop in and take his customers. Maybe automakers would decide they want to be in the business directly, even. People might sell vehicle conversion kits, which would also compete. Fred can't sit back and raise prices and expect to get anything he asks.
Of course, it's just a hypothetical story, but the point is that being the sole supplier, without the ability to force people to buy from you—or stop competition with patents or favorable (unfair) regulation and other artificial force-backed barriers—a monopoly is not necessarily a bad thing for customers.
(A theory exists called "predatory pricing" where companies lower prices so they're losing money to put competitors out of business, then raise them above the former price to make back the money. It has a number of flaws, one of which is, IIRC, is that it's never been observed in real life. I've heard of a chemical company that tried it—maybe in The Myth of the Robber Barons; the competition bought up their product at the low price and sold it in another market at a profit. The true "Robber Barons" were the ones that used the force of the state to guarantee them a market.) (DBR)
When businesses are accused of being monopolies (frequently falsely, and never through violence), that's bad; but the state, a violently-maintained monopoly in all sorts of essential services, is held up by those same people as ultimate good. Choice is the answer; remove government as violently-maintained (and funded) monopoly; relegate it to the role of just another service provider among competing others, and there is a chance for true accountability and choice. (DBR)