This post will focus on 2D game engines, because currently the games that I make are all 2D games.
A few of 2D game engines for Android that I know :
This is the engine I choose, because it has a lot of features(such as network for multiplayer, multitouch support, box2d physics engine integration), and their community is very alive, you can find answers to almost all of your problem with AndEngine in their forum.
This is a port of the popular 2D engine for iOS development. If you already have experience developing games in iOS using this engine, you should try this engine for Android.
This is a popular engine for Flash game development, now on Android. You should try this if you already have experience in Flash game development.
Based on a few reviews that I had found, this is also a good engine to try. It has a lot of neat features, including box2d integration, and according to this article, it has better performance than AndEngine. Honestly, I haven't tried this engine yet as I am currently happy with AndEngine.
This is a great 3D engine that you can also use to easily make 2D games. The only problem : it's expensive... to be able to make Android games, you need Android license (US$1500) on top of the professional license (US$1500). Soooo... you need US$3000 to be able to create games on Android using Unity3D. But this is a great engine, you can make game on one platform, and switch that game to another platform with just a single click of a button, but only if you have the money to pay for the license...
Based on my experience last month, this engine has horrible documentation, horrible support, abysmal community full of spam. But that was one month ago, so I don't know the current situation. I have already lost all interest in this engine.
That's all the 2D game engines that I know of.
If any of you know any other Android 2D game engines that is worth mentioning, don't hesitate to share it in here.