What public animation file formats are there available for 2D games? I'd like to know about both formats for procedural/skeletal animation, as well as traditional animation.
I have never seen an animation file format (animation meta data, etc) that was public. I made my own from scratch. It's based on XML and I load it using tinyXML. It pretty much says where bones move to from where, at which time, over what time. Honestly not much more than that, and yet it's plenty powerful. This is for as far as skeletal goes. But for something that's not, I would go with a sprite sheet and have a meta data file about the bounds for each frame, and how many frames in total, etc.
EDIT: PS, the actual animations of my game are mostly procedural, so that data is almost all an animation file is, and then it's animated in game.
Honestly this is a question that could have lots of broad answers. But here's mine.
There is PNG variant called MNG that supports frame-based animation. As for skeleton animations, I'm afraid you have to develop your own file format and encoder. The wise approach would be to prepare data in your games engine format, so loading skeletons would require no pre-processing.