This type of thread will eventually come up in software forums in general (why this solution for what they want to do), so I thought it would be good to collect everyone's reasons why they made Godot their solution for making games.
For me, I started making 2D games in GameMaker when I was 14 years old, but in reality I wanted to make games that were 3D (but the 3D solutions back were either just a programming language or very expensive). Over 20 games later, i found that Blender had a game engine and moved over to it.
It turned out that the BGE back in version 2.3x was not that great, it had (mediocre) physics and very limited graphics. I took a break from making games until that engine got an active developer who fixed the bugs and made it into an engine where many things started to just work. I then made full 3D games with it as it ascended to its peak in version 2.49.
Starting in version 2.59, the BGE started to see a decline in functionality that actually worked, but I at least was able to make games that work until version 2.69. After that, functionality started breaking at a fair clip and it got to where a lot of time was being spent fighting bugs, it really sapped the idea of continuing those projects as I didn't know if it will just crash when starting the engine (in a new version) when it worked fine before (this was when its development came almost to a complete stop and was accumulating far more bugs than were being fixed).
It got to the point where the most popular discussions among BGE users was the engine's future, it was to the point where I could no longer defend it because of how broken it became and how many people who wanted to get into the code ultimately ran away from it.
Now for one thing, I didn't want to go to Unity because of how it needed a separate IDE and how you needed to deal with limitations if you got the free version. Another factor was that I didn't want to be dependent on whether Autodesk wanted to make the .fbx format play nice with Blender. That was also a reason against Unreal 4, though the other one then is that it seemed to be a very heavy engine that required a very high-end PC.
Then I remembered a thread about the Godot engine being Open Sourced and went to its website, the first official version in the FOSS era was at RC1 so I decided to give it a shot. After some initial struggle, I liked how easy it was to create game logic with GDscript and how much of the functionality just worked out of the box. I also liked how it had visual tools for things like path creation and how easy it was to make things like material data unique for each instance. Then there was the innovative approach that is removing the line between prefabs and scenes, the insane setup possibilities you can do with them, and the lack of dealing with bugs and how many end up getting fixed (especially when hearing Unity and Unreal becoming known for bugs and users spending a lot of time on workarounds). There were some limitations alright (such as in physics and 3D), but now I'm using a 3.1 development build and the engine is in its best form yet.
A couple years later, I do not regret choosing Godot it when considering how even UPBGE, the last ditch effort to save the engine, has now been abandoned and sealing that solution's fate (replaced by a less game-centric interactive animation/prototyping tool in 2.8).
Phew, what was your reason for choosing Godot, what encouraged you to use it amid the other options that are out there?