The only dis/advantages in what your first language are purely pedagogical. It will dictate how you learn certain concepts. If you are starting a BSc. in CS, esp under the education system in Denmark, you will find that language selection will be the farthest thought from your mind by your senior year when you are looking for a job. All medium-to-high-level languages that descend from C have similar syntax, and transitioning from one to the other is fairly intuitive with a little bit of documentation.
The more important thing to learn, especially in undergraduate Computer Science, is programming techniques and theory (and don't neglect your math classes, they will provide more than you think). Program a lot, develop good habits, and know what the source code on your screen really means. Most software developers suck at this. They know a few languages, and maybe a few APIs. They very rarely understand the distinction between strongly typed and weakly typed languages, between lexical and dynamic scoping, between statically and dynamically typed languages, type safe versus non type safe, call by value versus call by reference versus call by need. When you understand these concepts, understanding the basics of any programming language only takes a few days of study (learning more takes more time, obviously).
People here talk about what the "industry" is doing. bronxbomber 92 claims C++ is THE language. I don't know what industry he is talking about, but I can tell you that you will see a lot more than JUST C++. You will see C, you will see Java, you will see Python, and probably a lot more (I worked on a project that involved Perl, C++, and C all in one application).
I can tell you that high paid software engineers transition gracefully across the platforms that change, and they change a lot. Java, C# and .NET, etc are all fads. They're important and relevant now, and it is worth the time to learn them to make yourself marketable. But, don't depend on your college education to give it to you. They will give you the tools to learn these things quite on your own or through internships or early jobs. And expect to see newer technologies that will exist alongside or replace these platforms and languages.
A lot of people think that the language matters and that you must start from square one with each language, or that one language will beat all, or that even one CLASS of languages will beat all. This is not the case. Most of these people are code monkeys that write poor code (and indeed, are the reason for the majority of software awfulness out there).
Keep in mind also that language is one aspect of the issue, and the other is platform. I have done operating system programming and GUI programming in C++. DRASTICALLY different, involving different libraries, etc. C# is a language that is made specifically for .NET, and learning the language is not the same as the platform on which it runs (I can write objects and methods in C# in my sleep, I am only right now getting comfortable with using them in the context of the .NET platform). Platforms change even more than languages. Don't worry about the "right" one, you'll see a variety of them over the course of your career. Learn the concepts behind them and you will find picking them up is much easier as you encounter them.