C++ is a fine language to learn, and as long as you keep in mind that it will be a long and twisty road to get through it, you should be fine. It is not an easy language, and C++11 certainly has not improved the number of corner cases at all. That being said... as long as you're learning modern C++ you should be fine in the long run. That being said, you do not need to use C++ to write games, you can write games in ANY programming language.
The thing to keep in mind is that C++ is one of the most difficult programming languages in use today. However, if you are willing to put in the extra time, it will be worth it. Someone who really understand C++ can transition to most other languages (expect functional) with ease. C# will be a lot easier to understand if you know C++.
Some languages will be easier to pick up on, yes. But in reality its not about "learning C++ makes you good at learning other languages." Its about the fact that learning any programming language... and more importantly the ART of programming, which is language agnostic, will enable you to more easily pick up future languages.
But it doesn't work the other way. Take someone who knows C#, or Java, or Javascript, and show them some C++ code. They will not understand it.
I have met (and hired) many programmers with a diverse number of backgrounds, and frankly... pretty much every single one of them could parse any program in any language. They might not know the SPECIFICS of what is going on, but they can reason their way through it and figure out what the program does and even how to modify it. C++ doesn't magically make you better at this.
And someone correct me if I'm wrong, but C++ is still the most used language for game programming.
Yes, but not due to performance reasons or any of the other common excuses people give. Frankly, its more that there just isn't another language out there that is A) supported on all of your target platforms and B) supports all of your legacy frameworks and existing code artifacts. When you have an enormous amount of pre-existing code and tools to work with, then you will find that most businesses are not interested in moving to another platform where they're going to have to rewrite or port a large portion of that code. You also have the simple problem of: If you're shipping a console game... it needs to be in a language that the compiler for the console supports. In general that's C and C++.