As per the answers in this question, public API was a priority for Jeff, back in August.
I'd like to know when it will be available.
Sometime this year. Ideally sooner rather than later. It is a high priority, but I have a lot on my mind grapes.
Update: now in private beta, and will remain so for 30-60 days so we make sure we get it right for V1. We don't want to go public until we feel confident it's right. Email email@example.com with your intended use case if you want to contribute.
I applaud the team for taking a whole 9 months to get it right, rather than rushing something out in 6-8 weeks. Once you release a "supported" api, it's very hard to change it — much more so even than interface features or reputation scoring on the main site.
This is assuming, of course, that they did get it right. That's even harder than making changes after release.