There was a talk on TED recently about using games to solve real world problems which is not a new idea, of course, but one which is not yet utilized to its full extent. There is Google Image Labeler and similar tools, however I don't usually hear about other, more complex applications.
For example, imagine a game of fighting the AIDS virus. The main enemy of the game has similar capabilities as the virus and the players can use the tools we have at our disposal to fight it. The goal is to defeat the enemy any way they can and if they succeed researchers can analyze the strategies of successful players when looking for new approaches in virus research. This way people who have no experience or interest in virology could help solve problems in the field without even knowing it if the problem is effectively and engagingly modeled (disguised) as a game.
Modeling the problem in a useful way is not easy and attacking the whole AIDS-cure problem in one game is probably not the way to go. AIDS research is a complex area which can be broken down to numerous small problems, so these individual smaller problems could be modeled as games. Even if only a partial breakthrough can be achieved with these games it can be a great leap forward in fighting of the disease. And AIDS is only an example, this approach could be used to solve any problem if we get the modeling right.
After watching the TED talk mentioned above I was a bit disappointed. The speaker came up with examples like a game about saving the world from oil shortage. This can also be useful, but I doubt the average gamer will be particularly excited to play with it. The important thing is to dress up the game as something else. Make it an RPG in which the gamers can be in their usual environment and they don't even have to know they are solving hard problems while playing.
Naturally, modeling the task in a fantasy setting is not trivial, but it pays off in the long run if it makes it possible to employ lots of young and motivated minds to solve hard problems. I can image a World of Warcraft extension which adds a new mission to the game modeling some problem with monsters and castles and such. It doesn't matter if it's hard. Dedicated players like hard tasks and it can even motivate them even more to make it to the end.
I don't know if somebody somewhere is already working on a game like this, but I hope so, because then in the not so near future the most pressing problems of the world can be solved by amateurs playing at home without even knowing about it. It will be like SETI@Home, only this application will use the idle capacity of human brains instead of computers and the user of the brain will even have fun as a side effect. :)