[Unity] - 3D and 2D Game engine with free tiers, focus on flexibility and customization. Write in C#, does have node-based scripting package. Good for cross-platform utility development.
[Unreal] - 3D and 2D Game engine with free tiers, focus high fidelity graphics and first person content. Write in Blueprints (node based) or C++. Good for creating cinematics or art showcases.
[Defold] - Free 2D game engine focused on web and mobile, cross platform. Uses Lua. Good for lightweight creation, frequent updates. Supported heavily by King (candy crush creator). Good for 2D content editing or game jam style creation.
[Love2D] - Free 2D Open source game engine framework designed for easy distribution. Uses Lua. Good for mechanic prototyping or small game jam style creation.
[Godot] - Free open-source 3D and 2D engine developed by a non-profit organization, funded by users. Of all engines mentioned, this is the most "Open"
[Cocos] - Free light-weight C++ flavored cross platform engine with a focus on mobile-style game content. Notably fewer integration than unity and unreal, but no cost. While it can do both 2D and 3D, it has a 2D focus.
[Itch.io] - A space to host, post, and distribute both free and paid games, tools, or other creations.