Recs.
Updated
Godot is free(libre), open source, MIT license, no royalties, 2D, 3D game engine full-featured. You can make any kind of complex games.
SpecsUpdate
Pros
Pro Free and open source
Godot is licensed under MIT license. Anyone can grab the source from https://github.com/godotengine/godot and compile the engine him/herself.
Pro Active development
This engine barely released one year ago has more than 1000 forks on github and about 100 developers. Not only that just a bit of browsing trough issues you will quickly find out the dev community loves new esp free technology and does not shy away from completely rewriting parts of the engine. By feb 2016 Vulkan will be supported including a complete 3D engine overhaul. The audio engine is being completely rewritten to use threads and so forth.
Pro Easy to learn scripting language
Godot has their own scripting language called GDscript. The scripting language is easy to learn with python-like format, but it is not python. More like a mix of Javascript, PHP, C++. It's very powerful, easy to learn, and it's free of unnecessary things because it's designed for this purpose.
It can be used to add custom behaviors to any object by extending it with scripting, using the built-in editor with syntax highlighting and code completion.
A built-in debugger with breakpoints and stepping can be used and graphs for possible bottlenecks can be checked.
Pro Friendly towards Version Control Systems
The engine is built not only to support version control but to really use it. Scene files for example which usually get compiled into some sort of unreadable data stay in a text format - that way you can actually see your changes in a version control system like Git.
Pro Internationalization of the editor
You can change the language shown in menus. Godot translations.
Pro Built-in documentation linked to the internal ScriptEditor
The editor has a fully searchable index of class API documentation for everything the engine offers (NOT just a web interface). You can easily open the documentation for any class by Ctrl-clicking the class's name in the in-engine text editor for scripts.
Pro Under constant development
This engine barely released one year ago has more than 1000 forks on github and about 100 developers. Not only that just a bit of browsing trough issues you will quickly find out the dev community loves new esp free technology and does not shy away from completely rewriting parts of the engine. The audio engine is being completely rewritten to use threads and so forth.
Pro Simple and readable codebase
The engine's source code is easy to read and understand with a self-documenting approach to code design. You don't have to wait months or years for other people to fix an engine bug that is important to your game. Often times, you can spend an hour or two of your own time to fix whatever problems you encounter yourself.
Pro Easily expanded scripting system
With 3.0's addition of NativeScript and PluginScript via GDNative, developers can easily define bindings for new scripting languages. In addition to the primarily supported C++, GDScript, VisualScript, and C# languages, the community has contributed D, Nim, and Python as well with more on the way.
Cons
Con Needs GPU for 2D
Not optimized for 2D operations without GPU. But see https://github.com/godotengine/godot/issues/3634 for an attempt to at least make it run there.
Con Self-designed scripting language
Implementing new scripting language instead of using an existing scripting engine (such as Lua or V8 JS) looks expensive, but easy to learn.
Con HTML5 exported games are slow
Godot uses Emscripten which emulates C++ code, which is ineffective and uses a lot of memory. Here are related issues https://github.com/godotengine/godot/issues?q=is%3Aissue+is%3Aopen+label%3Aplatform%3Ahtml5