There is a very interesting (and short paper) on the impact of and ease of illegal sharing of journal articles here.
For those of the tl;dr (too long didn't read) variety basically a large number of journals that practice closed access (you have to pay to read articles) are having their articles shared via websites etc. The estimated cost of one of these websites to the 2,000 odd journals whose articles were republished as $1.4Million (based on $30.00 per article).
I'm not a big fan of intellectual property (IP) laws (maybe because I have nothing to protect) but I feel that several things have come into play in recent years. The IP laws are now as likely to protect large companies from individuals as the opposite (in fact more likely as an individual will rarely have the resources to cover legal costs) and the rise of the internet which has blurred the line of what can actually be protected. Is code something that you can patent? that particular bit of code or the concept behind it. These issues have already been met by firstly music, then movies and now slowly the publishing world (look at the trouble google is having with news that they license and various books).
In the case of scientific publishing the real question is whether we should pay for information. Prior to the internet a lot of the work of publishers was exactly that: editing and publishing articles that would then be bound together and sent to those who were interested often costing a lot of money in the process. Now in the publishing world most of the work is done electronically, editing and organisation of the information is still important but the cost of actually printing the article is often no longer an issues as people will read the papers online. Should we then be paying up to $30 for an article?
I don't think we should. Information is at its best when everyone can access it, creating a situation in which multiple people can all review and learn from someone's contribution is far preferable to creating an arbitrary barrier for people to cross. This is especially true in the case of the sciences where people are interested but only a very minor percentage will want to pay up to $100 for a paper that they're only interested in browsing. The upshot of charging people to learn is that you create a capitalist market for information. On the internet this means that people will go where it's freely available (eg wikipedia) or where it's free but wrong (eg Answers in Genesis). As part of the purpose of science is the propagation of knowledge forcing people to pay to get good information seems counter-intuitive. This is more of a problem now when information is so freely available in general and people are treating science more and more like magic: either something to be feared or avoided as un-knowable. Giving good and easy access to genuine science will mean that those who are interested can get hold of the actual information that is needed and make their own mind up about it. I'm not saying this will stop websites like Age of autism from spreading misinformation but with access to genuine papers on vaccines or the LHC people who might otherwise take these websites at face value (especially when presented with the scientific world hiding its information behind a pay wall) they may read up and find out the real facts.
While this is a very similar situation to the one found in the entertainment industry I think the subtle differences make the case stronger for open access journals. While the entertainment industry should be free in some form (I pay for the cinema and yet still insists on adverts why!?) funded through pay-to-dodge ads or a pay-to-own system etc. The journals system should be completely free, a lot of journals already have adverts if these moved onto their websites in a "pay for the ad free premium version" system I would be more than happy.