Pollution is a href="http://www.amazon.com/exec/obidos/ASIN/0226111016/reasonmagazineA/">The Problem of Social Cost," begins with a shocking observation: "Externalities" are reciprocal. They aren't a matter of physical invasion, with good guys and bad guys, but of unpriced impacts of any sort. We may recognize that an action inflicts a spillover harm, but stopping that action inflicts a different spillover harm.
If I build an ugly house, your aesthetic sensibilities may be offended. But if, to keep the neighborhood to your taste, you stop me from building my house, I lose the benefit of living in it. If I buy a cool barbecue grill, you may feel pressure to do likewise. But if you keep me from buying the grill, or take my money in a consumption tax, I'm hurt by your efforts. The same is true for classic externalities: If a steel mill pollutes the air, it harms those who breathe the pollution. But to shut down the mill (or require controls that increase its costs) harms those who buy and sell steel. In all these cases, an externality exists either way, regardless of who has to bear the costs of adjustment. (There are other aspects to Coase's paper, including, famously, the important issue of transaction costs.)
To deal with externalities, therefore, Coase argues for putting the burden where the cost is least. In a Coasian world, people who don't like other people's garages avert their eyes. People who do not approve of violent movies do not buy tickets for them and, perhaps, do not socialize with others who do. People who covet other people's nice possessions get therapy or religion. In a Coasian world, you cannot simply yell "externality" and get the government to stamp out anything that offends you. You cannot declare that conjectural, unquantified costs, such as aesthetic considerations, are infinite, but real, private market costs, such as more expensive houses, don't count. The burden of proof for regulation is not infinite, but it is high.
By contrast, one reason for regulating stationary sources of gross air pollution, such as steel mills circa 1969, is that such regulation offers large benefits at relatively low costs. It would be extremely difficult for individuals to avoid inhaling the dirty air, compared to the relative ease with which the factory could install smokestack scrubbers or use cleaner coal.
Coase's reasoning is obviously not an absolutist argument for freedom of action. As Frank notes, even strong libertarians usually make exceptions for some sorts of externalities. By clarifying the issues, Coase's utilitarian insight helps separate serious spillovers from mere excuses for bossing people around.
There are certainly other arguments against the infinitely elastic notion of externalities, which, as a theoretical matter, is a prescription for totalitarian control. But Coase's insight explains in a nutshell why peaceful social life, in which all actions are necessarily interconnected, must include a large measure of tolerance--and why spouting economic jargon is no substitute for thinking clearly.