First off, the term "free market" isn't a very good one, since a basic tenet of economics is that everything has to be paid for somehow. The actual markets aren't unrestrained, either - a market economy depends on restrictions on coercion and cheating. "Competitive market" would be a much better term in my opinion, but, whatever. Anyway, "free market" refers to a model, or an ideal system in which firms and individuals act in their own best interest, and goods are distributed according to supply and demand. That's not much of a description, so let's go over what is required for a free market. First is competition. This assumes that firms are forced to offer the best deal they can afford to, or they'll be run out of business by another firm that's willing to accept lower margins. This is in the long run, of course, and it depends on another assumption, "zero barriers to entry". This means that new firms can enter a market without restriction. Now, it's clear that this is an unrealistic assumption. It takes a lot of money to start a business, even a small one, and a lot of markets have "economies of scale" where costs go down as you produce more, so you can't really enter the market as a small firm. This is where capitalism comes in. By providing the startup costs, investors make it much easier for an entrepreneur to start a new firm. And, with limited liability corporations, if the firm tanks, the entrepreneur doesn't have to cover its debts, which removes a huge disincentive to firm creation. The purpose of investment capital and corporations are to make our market system approximate more closely the free market ideal.
First, remember what a market system is for: optimizing the economy. However, optimization isn't a linear thing. You can't just optimize a car, for example, you have to choose to optimize it for acceleration, handling, safety, cost, emissions, style, etc. In reality, you don't choose just one parameter to optimize, you assign emphasis to each one. And, just like each person will have a different set of priorities they consider when choosing a car, each economy has different market forces that determine how it is optimized. Part of this is the preferences of the consumers, but a very large part of it is the effect of the government, which sets the rules for how firms can compete. If you want an idea of how market competition would go in a truly "free" market, look at the illegal drug market. Since they operate outside of the law, they really don't have any restrictions on how they operate, other than some procedural restrictions they must enact themselves to avoid being caught. As a result, the main mode of competition is military - powerful "firms" destroy their competition so they can get higher margins by not engaging in price competition. Now, you may not like my analogy, but the point is that we don't want firms competing in this way. I don't think it's much of a stretch to claim that only government regulation can prevent this type of competition. You could claim that this isn't really an argument for government regulation, because preventing the murder of competition isn't really regulation of business, it's just universal application of the "prevent murder" function of government. That's a fair statement, but it still shows that a government can't help but affect the market forces that govern an economy.
The next function I'm going to look at is more invasive, however. As is, the government offers enforcement of patents and copyrights to firms and individuals. Right now, with the whole mp3 vs. RIAA thing, it should be clear that this function of government has a profound effect on our economy. More interestingly for this discussion, however, is the effect of patent law. The government offers protection of a patent for seven years, I think. During this time, the patent holder has a monopoly on that product, and is free to charge whatever they want without worrying about being undercut by firms who don't have any research costs to pay off. After the patent expires, though, generic versions become legal, the former patent holder has to face competition, and prices for the consumer go down. The effect of this is that the costs of research and development are offset by the high margins the patent holder can enjoy for the duration of their patent, so research and development are encouraged, but prices are still held down by market competition. Now, the seven-year patent duration is arbitrarily decided on by the government - it could easily be two years, or fifty. If it was fifty, companies would be investing a lot more in research, but comsumer costs would be higher and efficiency would be lower, since companies ould face less incentive to optimize their prduction processes. Likewise, if it was two years, costs would be lower, but a lot less research would get done, since it would not be as profitable, so we would probably be at a much lower technological level than we are now.
The observation that government has set the patent term at seven years is very important, because it shows that the government has limited property rights for the sake of an efficient economy. Patents are intellectual property, but if they never expired, a competitive market system would be impossible - excepting farm produce, wood, and such, every product would be supplied by a monopoly. Since "pro-business" supporters of our current not-really-free market system generally hold property rights to be sacrosanct, and rely on this for much of their arguments, the practical necessity of limiting property rights is an important observation.
Our system relies on the competition of firms to keep prices down and production efficient, but these benefits only come from one form of competition out of several. I'll call the form of competition where companies try to gain a larger share of the market (meaning that they sell a larger percent of the total amount of a particular type of product) by offering lower costs and/or a better product constructive competition. We already went over military competition, where firms attempt to destroy one another, in the previous section. This is a destructive mode of competition, since it lowers total efficiency by reducing the victim firm's ability to produce, and it raises prices beyond simply adding to the overhead of the aggressor firm. Another mode of competition is informational competition, in which engaging firms seek to make consumers more aware of, or more favorable toward their product, independent of its merits. In a word, advertising.
Advertising has two functions: to make consumers aware of a product's merits (to want it rationally), and to form some kind of favorable association (to want it irrationally). An example of the first would be the part of car commercials in which they give numbers describing the vehicle's performance, or just show a picture of it so you know what it looks like. An example of the second would be the part of the car commercial where the car is driving through the desert, climbing a mountain, on the moon, or something else adventurous and unrealistic; or when an athlete or some such high-status individual endorses the product. Of the two, the second is far more prevalent, because, in general, it makes more money for the engaging firm. However, this type of advertising adds nothing to the efficiency of the market, and leads consumers toward products that are less competitive in terms of actual value. If the government put some restrictions on advertising, say, only factual statements that pertain to the performance/cost of the product, and only showing products in their intended use, the efficiency of the market would go up. Entertainment in general would get more expensive, and Network TV and print magazines would probably cease to exist entirely, but since the internet exists now, that wouldn't be all that bad. Of course, you'd never be able to pass such a resolution, since there's a lot of money tied up in the whole business, and politicians can get people pretty riled up about the government putting any kind of restrictions on behaviour when religion isn't involved. Maybe if you used some sort of "for the children" approach, like they do with violent video games. It's hard to demonize something that exists within the mainstream culture, though, so you'd have to create the image of some kind of advertising subculture for the average american to fear.