AndEngine is a free Android 2D OpenGL game engine. Developed by Nicolas Gramlich, it is one of the most popular game engines to build games for the Android platform. AndEngine supports extensions that add additional capability to the game engine. Some of the popular extensions are the Physics Box2D, Live Wallpaper, Multiplayer Extension etc.
There is an AndEngine app you can download from the play store that demos the capabilities of the game engine. The demo app is also open source and is available in their github repo.
New to AndEngine? Try These Useful AndEngine Tutorials