I am currently using Urho3D:

•  Because it runs on my low-config system .
•  lightweight and powerful, has all features of a game engine .
• -modern c++ style .
• -neat and simple coding style .
• helpful community.

My first choice was UDK, ages ago  Later I has been working for 2 years for company creating games in Unity. Shipping mobile games with Unity is super efficient and easy but creating third-person shooter was a nightmare.

I see many people saying: 'Oh I like this engine because I can do everything with it'. But remember that it also sometimes means: 'you have to do everything to actually achieve anything with it'. So using UE4 makes live easier if you can just grab all the ready stuff and after a day, finish your level with all logic, terrain and a proper lighting. I think that's very important.

Anyway checkout my: Flax Engine  Oh, and here is open source C# API and Editor: GitHub

A few months ago i gave unreal engine 4 a try and made a simple 2D platforming game and was really impressed how fast you get a game up and running, especially when you use blueprints. I loved the material system, it is much better using a node-based system than writing all the shaders yourself. But after i digged down more into 2D and increased the complexity of my game - i started to dislike the way unreal engine 4 does 2D. Especially after it crashed my tilemap and re-position/re-scaled everything + a broken git plugin which i was heavy rely on... Also there was more which i didnt´t like:

- The tilemap editor is separted from the editor itself and there is no concept of placing/integrating objects in tiles. When i move/scale the tilemap i want all objects to move as well
- There is no concept of using multiple tilemaps with different tile sizes (finer or rougher) in the same grid. Sure you can place your second/third tiles behind/infront of the other but then it gets very hard to manipule placed objects.
- 2D lighting integration was barely working, maybe it is working now? Last version i used was 4.13
- Mass importing 2D sprites/animations was a hassle, but it was not that bad.

After all it seems unreal engine 4 is not really suited for a 2D tilebased game, but may be great for other kind of games.

I would really like to get back to it, but i am afraid that the 2D integration gets worse on each version...
Maybe i should drop 2D entirely and start to go full 3D...
After all unreal engine 4 core strength is its awesome lighting and material system.

Right now, i have my own c++ framework which powers my game, but its still on a very early state...

Home made engine.

I'm happy with my choice but note that this is a very tricky choice and, as a rule of thumb, I would not recommend using your own engine. Why it works for me? Well, first I'm an old geezer and I have been making this engine since Amiga, so making a new iteration of it was cheaper and more convienent to me than learning a new one. Second, I have my old habits and I'm unwilling to change them And third, the most important, I limit myself to certain types of games which are suitable for my engine (2D, turn based). Oh yes, also I'm doing it full time and I use it for several games, so the time to write the engine is "amortized" between several projects (if I were to use it for one game it would make no sense at all, using premade one would be better).

Advantages: extremely easy & convenient to use (since it has a very limited usability, exactly what I need, no generic stuff), control over new version (no Unity like horror stories), very fast (for it's purpose), runs on ancient hardware without lags, it's 2D (and there are no decent 2D engines anyway).

Disadvantages: quite a lot, like I need to patch it and upgrade myself

I personally don't use any game engines because I like to have full control/flexibility on what I can do to the game.

Although you can still do the same things with a game engine, when you are programming at the lowest-level,

you really feel a lot of freedom on what you are doing, especially AI stuff.

I have been using the xna and more recently the monogame frameworks. These options provide a high level of code for tasks that i just prefer not to deal with such as image loading, sounds and so forth. With these tools it makes it quick to produce your item engine with as much flexibility that you need. Running in dot net gives out the added bonus of being pretty efficient. I'm not a huge fan of all in one editors such as unity. I feel to separated from the code at times and i feel it takes a much larger learning curve to pick up on a full engine rather than brewing something in house where you only have to focus on the pieces you need. That being dai said i do feel that monogame and mono have some draw backs. I would prefer to do all of my development in Linux and release and compile for Android, linux and Windows but I just came get xamarin.android to compile and work with Linux. Other than that i am very happy with it. I'm surprised i dont see more people using monogame. It's probably the easiest and cleanest framework to use when developing 2D games.