I tend to think of piracy as a demonstration that a business model is broken and is not offering people the services they want at a price they’re willing to pay. Usually, the company maintains this model because they believe there is more money for them in it; and they may be right, for example most people would buy Windows if it was $50 but Microsoft probably makes more money selling the quantity they do at $300.
With software I think that how you change your business model really depends on what market segment you’re in, and there is not a one size fits all option. With
music and movies I think they should pass on the manufacturing, distribution and retail savings onto the customer and encourage them to spend the same amount on music as they did before Napster while getting far more music; if you are averaging 1 Million people buying 1 album on itunes for $15 a month, you would be doing a lot better if you had 20 Million people buying 5 albums for $15 a month. At some point the price becomes low enough that the convenience of buying something legally is worth the cost.
With videogames I would suggest a modified shareware/episodic content business model. Basically, give someone a big chunk of the single-player mode (like 1/6 or 1/3 of the game), and a couple of multiplayer modes with single maps for random games, all for free or for a low price and then charge a reasonable price to buy the full game with additional modes (like co-op). The reason I say this is that in my experience most pirates don’t play more than an hour or two on the vast majority of their games, and I suspect that if they were still enjoying themselves at the end of your shareware version you could likely convert them into a sale.