Ambiera Coppercube (Studio version, bought in Steam) good for games with a PS2 like aesthetic. It has a free version, the programing is realy simple it use a visual system (not node based like Unreal's that can be improved using Javascript and a API that is small and well documented.
UPBGE for games with a more 'modern look' since is has better dynamic lighting, realtime reflections, etc. (So for more 'modern graphics')
UPBGE is a modified Blender. It allows modeling, animating and so inside the tool. The programing can be done in Logic bricks (a classic method from old blendes) or Logic nodes (need to activate in the preferences, is like the unreal's blueprint but way more easy to use.) Or Python (personally i dislike it.)
Also i like to play with FPS Creator or GameGuruMax from time to time if i want to make a simple FPS.
Good if you want to tell a story without the need to reinvent the wheel since basic controls and save/load game are already implemented.