As Mitch said, spine-libgdx gets things implemented first and gets a lot of testing since Spine itself uses it. I am also the co-author of libgdx and I actively manage and contribute to that project, so obviously it is very highly recommended. It can deploy to Windows, Mac, Linux, HTML5, iOS, and Android.
He is also right about spine-unity being pretty freaking great! Check out some of what it can do:
viewtopic.php?f=3&t=3318
The official runtimes are officially supported:
http://esotericsoftware.com/spine-runtimes
The current state of things is that spine-as3, spine-lua, and spine-js are missing flip timelines (not other runtimes extend these, so are also missing flip), but it will be done soon. spine-corona is long, long overdue for an update (sorry again guys! 🙁), I have started working on it but other issues keep popping up. spine-love and spine-turbulenz are missing meshes.