Recs.
Updated
Godot is an advanced, feature packed, multi-platform 2D and 3D game engine. It provides a huge set of common tools, so you can just focus on making your game.
Godot is completely free and open source under the very permissive MIT license. No strings attached, no royalties, nothing. Your game is yours, down to the last line of engine code.
SpecsUpdate
Pros
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 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 Internationalization of the editor
You can change the language shown in menus. Godot translations.
Cons
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.
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 Primarily supports own proprietary language (GD Script)
While it's very accessible, and if you know Python you'll pick it up fast, having to learn a new language to fully make use of the platform can be a bit discouraging. And for those learning to code as well as learning Godot for the first time, many would rather learn a language they can 'take with them' when they explore other platforms in the future.
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.