Legend:
2D = Recommended for two-dimensional games
3D = Recommended for three-dimensional games
NC = Recommended for newcomers and beginners
OS = Open Source
{} = Languages used

GameMaker:
[2D; NC; {Drag'n'Drop, GML}]
yoyogames.com/gamemaker

Godot:
[2D; OS; {C++, GDScript}]
godotengine.org

Haxe:
[2D; {AS3}]
haxeflixel.com

LÖVE:
[2D; NC; OS; {Lua}]
love2d.org

UE4:
[3D; OS; {Blueprints, C++}]
unrealengine.com

Unity:
[2D; 3D; {C#}]
unity3d.com