There are some useful free and open source game engines available for Android developers that help you to develop games with high performance.
Angle
This project is aimed to be a way to develop 2D games using OpenGL ES on Android providing as much speed as possible. The engine is entirely coded in java so you can overload every object for your convenience.
AndEngine
AndEngine is a free 2D OpenGL Game Engine for the Android platform with following features. You can find many examples from here.
Android-Optimized
Android 1.6 Compatibility
SplitScreen
Network Multiplayer
Live-Wallpapers
MultiTouch
Physics-Engine (Box2D)
libgdx
Libgdx a cross-platform Java game development framework based on OpenGL (ES) which written in Java with some JNI code for performance hungry sections.
Catcake
Catcake is a cross-platform 3D graphics engine intended to be easy-to-use and high performance, which also supports the features for game development, such as animation, input device handling, and sound playing, it runs on Windows, Linux, and Android.
jPCT-AE
If you are already familiar with jPCT, you should have known it. jPCT-AE is an open source 3D engine for Android, it’s a port of jPCT to Android.
Alien3d
Alien3D is an OpenGL ES based game for Android. Some samples can be found here. It seems this project was stopped since 2009.
Rokon
Rokon is an open source game engine for Android based OpenGL ES. Unfortunately, the author stopped to maintain this project. If you only want to know something about the game engine, you also can download and read the source.