You need to learn several languages to be a top-class programmer.

C, C#, C++, Java, Python. These are all important. But I must say, some users have pretty much said it all.

Why python and C? C#, C++, Java sound useful..........I want to be a game developer but I also want to be able to make simple apps. I started off programming apps in Visual Basic and FORTRAN but right now I'm working on a game with C-Script. Not really interested in web stuff.

Yeah I guess if you're doing C++ then C isn't necessary. I actually hate C as it just ends up being a pain in the ass at the end of the day.

Otherwise, I just know that my buddies try and work with several languages as flexibility is key in the software world. The python I mentioned since I'm working with that and half the web is written in python, but since you say you're not interested in web stuff that's also not necessary I guess.

Rather listen to Rainbird

1. Which language is more widely used?
They are close. According to TIOBE Programming Community Index for August 2011
C++ is at N3 with 8.433% and C# is at N5 with 6.042%.
2. Which is easier to learn and use?
C# is easier to learn and use. C# is clean, powerful and modern language. Better then Java IMO. C++ is old, more difficult, not so clean and need more skills, but very powerful.
3. Which is better to learn for game development?
C++. C# and Java can be used, but C++ is the standard. Game development has two critical areas - memory and speed. C# and Java sacrifice both of them for other benefits as - easy to write and use.
4. Which is better to learn for software, programs and app development?
If memory and speed are not critical as in game development - C#. With C# you can write complex apps much faster and with less efforts.
5. What's the major difference between them, anyway?
Both C++ and C# are object-oriented programming languages. Their syntax is very similar. C++ is regarded as a mid-level language. C# aims to combine the high productivity of high-level programming languages and the raw power of C++. C# is designed to free the developers from the task of doing memory management.

I have 10 years of C++, Java, C# and PHP programing experience. For different tasks a different language is better, but if you know C++ it is very easy to switch to Java, C# or PHP.

Python is very useful for AI. I loved my AI studies and python is the leading language for that... AFAIK.

Python is just lovely to use. It lacks the versatility of Java and you cannot interact with the machine nearly as well as in C++ but everything is just nice in Python. For game development I believe Python is fairly often used for scripting. It's definitely one you want to pick up eventually.

C is useful for a few things, embedded systems are usually programmed in C or assembly (and C is nicer than assembly) for example. Also because it's quite low level you can optimise more thoroughly in C if you're into that stuff.

Edit: I'd personally advice learning C++ or Java, once you learn one of those two the others should come more easily. I wouldn't learn Python first because then you might get into the habit of thinking everything is going to be dynamically typed.

BTW if you want to write some "made by me" games - XNA with C# is very good for this job.

C may be a pain in the ass but if you have a good undestanding of it, it will make you that much better at C++.

Personally, I would say research all the different types of languages and learn at least one of each.  While you're learning those languages, start diving into the theory.  If you can make a bubble sort in one language you know, you can make it in another language, it's just knowing how, why, and when to use the particular algorithm is important.

For object oriented definately go with C/C++, those are a given.  For functional type languages (great for AI), go with Python and Lua.  Meanwhile start delving into thingsl ike VB.Net and C#.  If you're feeling particularly daring start having fun with assembly language.  There are loads more of things out there to learn too.  What type of programing do you want to do?

I wouldn't worry myself with Java anymore.  It's definately worth taking a look at and making a few simple programs to say yeah, I've used it but not much beyond that.  It's slow and nobody in and out of game development really uses it anymore.

Also, again just because it can't be stressed enough, take lots of math and physics classes.  They're nearly as important as the programming.