What is C# capable of?

You can basically write any type of application using C# except the following:

1. Kernel mode programs such as device drivers. These are ruled out because the CLR can only run in user mode.

2. Critical real time applications. These are difficult to write because of the risk that the garbage collector may kick in whilst the program is in the middle of a critical operation. However, you can minimize this risk by forcing a collection (with GC.Collect) before the critical operations start.

Performance is typically about 80-90% of an equivalent C/C++ application though judicious use of unsafe code (which effectively turns off string and array bounds checking) can close the gap somewhat. The performance difference tends to only be noticeable in games or processor intensive applications.

On the plus side, applications can generally be developed much more quickly with C# than C/C++ and are easier to maintain. The programmer is relieved of the responsibility for memory management which is take care of by the CLR. The use of pointers is unnecessary (except in unsafe code) and C#'s compilation model doesn't require forward references to types which haven't yet been declared.  

C# is also suitable for writing very large applications because of it's strict object oriented nature and emphasis on component based development.