If you want to try your hand at 2D game, you can use
http://love2d.org/ . It's basically a lua game engine, which allows you to write games using lua scripts.
If you are fimiliar with C++ SFML (
http://www.sfml-dev.org/ ) provide a very good framework for games. It not a game engine, but has a lot of the basics required to write your own game, mainly resource loading (image, audio), video (opengl), input etc.