C++ and engines go together like acids and bases. Most engines are all about productivity, and C++ certainly doesn't fit that bill. C++ is more then language you would use to write the engine in the first place, but as an implementation layer, people generally will use something much higher level than C++.


That said, options exist.

CryEngine is C++ based and a peer to Unity.
Ogre 3D is C++ based, although not technically an engine, it's a 3D renderer/scenegraph. That said, if it was me personally working in C++ + 3D at this moment, this is what I'd choose.
IrrLicht is another option
Crystal Space has been kicking around for years too, but I don't really know if anything polished ever came out of it.


Then on the 2D side, you have:
SFML
SDL
Marmalade ( not really an engine, more a C++ middleware layer slight above OpenGL )
Allegro
Cave


Of course I am missing about half a hundred, to say nothing about obsolete engines like The Nebula Device ( which was really cool... ). If you are working on 2D, I have a SFML Tutorial/C++ language primer , that as an established C# programmer, should get you mostly up to speed on the language features. You will find a lot of them very frustrating coming from C++, be ready for a lot of "I have to do what????" and "theres no library for what???" moments in your near future.

That said, it's always kinda fun learning new languages.

Spend a few months with just C++ first. Try to really understand the language and its standard library. You'll be much less effective if you try to learn some game library/API/engine while trying to also learn C++'s quirks. And it has a lot of quirks and gotchas.

After that, which engine to use depends a lot on what kind of game you want to make. 2D? 3D? Mobile development, or PC?

[edit]

At first I panicked when I hit the post button and watched my post expand into something much larger than what I had written, I panicked, only to relax and realize I'd been ninja'd.

Switching to C++ from a syntax point of view will be tricky, but not the hardest thing out there. I suggest you first try to understand what a native language like c++ means. The biggest difference IMO is the manual memory management you have to do in c++, and that one will be quite daunting at first, because it is the root of most issues when developing native apps. Second, the standard library is nowhere near the one in .NET. It has way fewer functionality and it is not a platform itself. However, this is complemented by the tons of c++ libraries out there you can use in your projects.

I would first stay a bit away from game development and focus on learning the language well, and only then dive into graphics programming and games.

Hi everybody,
I'm a Unity3D programmer. I made more than one game in c# and I have much experience with that.
But now I would like to study C++ and I have a basic knowledgement of it. Can some c++ programmer or anybody tell me, which Engine should I use, or what's the solution for my request ?

Thank you,
Nikolai.

If you want to learn C++ then you shouldn't worry about which engine to use (You shouldn't make a big game using it to start with anyway), start with the basics then you can use a framework such as SDL or SFML and possibly add OpenGL if you want to learn 3D programming (Alternativly you can use Win32 and DirectX if you're on Windows).

Once you know C++ fairly well you should ask yourself if you want to learn low level engine programming or not.
If yes then you should just build a game using the low level APIs of your choice (OpenGL or DirectX usually) (Don't worry about making or using an engine, just make the game to start with and let the "so called engine" develop naturally)
If no then you should pick an engine that gets the job done and use whichever language it provides for you (Most likely this will not be C++ as the industry is moving towards higher level languages for high level programming) (Even CryEngine which has a C++ interface favors high level scripting using lua for large parts of the game logic)