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 Active development
UPDATE: There are currently 700+ contributors on Github
Although this engine is still pretty young, it 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 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 Internationalization of the editor
You can change the language shown in menus. Godot translations: https://hosted.weblate.org/projects/godot-engine/godot/
Pro Friendly towards Version Control Systems
The engine is build 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 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 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 Strange terminology at its base
Scenes can be made up of other scenes. That makes some sense. But even the smallest object (or prefab or asset) in a scene -- such as that spoon on the table or the marble on the floor -- is still called a scene... Except when it's called a node. This is a bit odd for those coming from other engines. With all the great decisions behind the basic design of this engine, the choice of this term from all the potential other terms out there seems really out of place and only serves as a constant reminder that not everything about Godot is great.
Con No console targets
Given that you can target both desktops and consoles with the same code base in other engines, the lack of support for consoles in Godot is pretty hard to get past if targeting desktops for a game. But asking for an open-source engine to target consoles is probably too much to ask. But it would be interesting to see some legacy consoles targeted even if current ones cannot be.
Con Slow and unadvanced 3D engine
Although the 2D engine in Godot is amazing, 3D is very slow, and lacks proper reflection materials.
Con Difficult to optimize
Godot has an OOP architecture. Everything is an object internally and data is spread among many classes, thus it's difficult to optimize (i.e. not cache friendly, difficuly to vectorize or paralellize, etc).
Read about "Data Oriented Design" for more info about the problems and solutions.
Recommendations
Comments
Flagged Pros + Cons
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 Unified game editor interface
All the game developing work is done inside one program: the engine editor. This feature is something only high end engines have. Even the scripting is done in the same program. No need for Eclipse or other front end editors.
Out of Date Pros + Cons
Con Poor tutorials and documentation
There are tutorials and there is a documentation, but as a novice, you can't really find enough stuff to learn it from the ground up. Though this may be only temporary because the community is getting bigger and bigger. V2.0 from Godot is only several months old, so there should be more tutorials and documentations with time.