It is possible to compile a C# app such that it has no dependencies on any of the built-in .NET types & libraries, by using the /nostdlib switch (see http://msdn.microsoft.com/en-us/library/fa13yay7.aspx). You then need to supply your own System namespace.
However, this doesn't remove the need for the .NET framework on the target machine if you use the standard C# compiler. As well as containing the built-in types, the framework also includes the JIT IL compiler, the CLR extra, which all .NET executables and dll's are reliant on.
There are ways of compiling C# code such that it doesn't need the framework though. The Xamarin product for example (http://xamarin.com/), supports compiling C# code to native iOS apps, which are wholely independent of the .NET framework. I'm not aware of any equivalent for "desktop" OS's though.