Recs.
Updated
Cocos2D-x is a complete toolchain for developing multi-platform games. Cross platform, fast, open source and free. Supports Skeletal Animation, Sprite Sheet Animation, Coordinate systems, Effects, multi resolution devices, Textures, Transitions, TileMaps and Particles. It adopts a RenderQueue design.
SpecsUpdate
Pros
Pro Supports 3D models with skeleton animation
A new feature since Cocos2d-x v3.1 is support for 3D models (in your 2D game), not only this but support for skeleton animations is included too! This awesome feature allows for impressive characters in your game along with easier, more fluid and realistic animations.
Pro Future-proof
Cocos2D-x is not only open source but also supported by Chukong Technologies of China and USA.
Regularly updated and adding support for the latest technologies. 2014 has already seen the release of Version 3, a new Cocos Studio development toolkit (optional) and support for new technologies like skeleton animation systems Spine and Adobe DragonBone.
Pro A proven engine for mobile development
According to the Cocos2D-x website, 25% of iPhone games are made using Cocos2D-x (A Cocos2D mobile variant.)
This means you will not be alone in development, and will have access to a large community and know you are developing for an engine that works.
Cons
Con Poor support and non-existent community
Up until 2013, this was one of the best engines around. However, since then it was bought by a Chinese company and began stagnating - it's virtually in a slow death. Most developers abandoned Cocos in favor of more modern solutions leaving the community weak and the forums with little or no traffic. Although the Cocos2d-x Forum seems to have a decent community going.
Con Poor documentation
Most existing documentation is out of date. API documentation sometimes exists, though is usually just a one-liner and more often than not is completely absent. New features and significant system rewrites often make it to a major release without a single line of documentation accompanying them.