I love andengine, and had make several games based on andengine. But, be honest, andengine is not fast enough for mobile game so today I tell you an alternative choice - Libgdx from badlogic company
Libgdx is high performance engine. The performance is much better cause it does not make opengl call before each render of object. The amazing part is Libgdx allow developer test their game on desktop as normal java application, instead of use a real mobile device. But you should still test at real mobile before you publish your game!
But, Andengine is a better choice for beginner. Why I said that? Andengine does much better on the game part, such as making some Sprite/TiledSprite class which give create help for developer. It's easier to understand and simple to control the game flow.
I'm still checking this engine and see if it is suitable for my next game. You know, the performance is quite important in mobile game developing...
Download from Google:
To quick start, download the helloworld example. It contains two project inside. One can be run in desktop and the other one can run in android(with ref to the 1st project)