The Yahoo Search Blog announced the release of the Yahoo Answers API. The API will allow developers to pull questions from the Yahoo Answers database by search, category, and user. You can even get the answers for those questions. More details at http://developer.yahoo.com/answers/.
Postscript: Jeremy Zawodny suggests to me that the Yahoo Answers API will soon allow writing to the Yahoo Answers database, and not just read only access. Niche answer social networks, here we come?