[lycidas]

I found that having problem statements does energize hackers. As a participant, I've seen a lot of people not having "cool" ideas to work on and instead ending up smashing together a bunch of API's or building another social share app.

To relate to your point of organizing purpose-based hackathons, I've helped organize a hackathon last year, in which we brought in NGO's and had them issue problem statements about specific problems in the third world. Then hackers were encouraged to try to solve these problems using tech. I was amazed at the results -- people had actually built something useful to the world outside the narrow 48-hour time window! And in the end, the programmers seemed happy that they were solving a real problem, of course doing it in their own "cool" way.