My opinion is C# and ASP.NET would be the best of the three for development that is web biased.
I doubt anyone writes new web apps in C or C++ anymore. It was done 10 years ago, and there's likely a lot of legacy code still in use, but they're not particularly well suited, there doesn't appear to be as much (ongoing) tool support, and they probably have a small active community that does web development (except perhaps for web server development). I wrote many website C++ COM objects back in the day, but C# is far more productive that there's no compelling reason to code C or C++ (in this context) unless you need to.
I do still write C++ if necessary, but it's typically for a small problem domain. e.g. communicating from C# via P/Invoke to old C-style dll's - doing some things that are downright clumsy in C# were a breeze to create a C++ COM object as a bridge.
The nice thing with C# is that you can also easily transfer into writing Windows and Console apps and stay in C#. With Mono you're also not limited to Windows (although you may be limited to which libraries you use).
Anyways this is all from a web-biased perspective. If you asked about embedded devices I'd say C or C++. You could argue none of these are suited for web development, but C#/ASP.NET is pretty slick, it works well, there are heaps of online resources, a huge community, and free dev tools.
So from a real-world perspective, picking only one of C#, C++ and C as requested, as a general rule, you're better to stick with C#.