There aren't many obvious practical uses for this, but they are out there and they do exist. We've come across the requirement a few times as consultants to enterprise organisations -- for example, a utility that gathers information on a wire that must only be running a single instance -- and it took us a while before we settled on the code to solve it.

We tried various methods -- broadcasting on sockets, named pipes, magic 'lock' files (this is the simplest solution, and the one that a lot of software uses -- it's effectively a file with a non-sharable lock -- if you can't lock the file, the app is already running). We finally came across the .NET Mutex class, and that fit our needs beautifully. You define a string which becomes your identifier, and then create a Mutex for that identifier. Mutex stands for Mutually Exclusive. If somebody else has Mutex'ed that identified, you'll get a fail. Here's the code to add to your static main method:

static void main(string[] args)
{
  string identifier = "MyApplicationIdentifier";
  bool ok;

  Mutex mutex = new Mutex(true, identifier, out ok);

  if (!ok)
  {
    // Message box provides visual feedback for this demo
    MessageBox.Show("This application is already running");
    return;
  }
  else
  {
    // This becomes your application's entry point
  }

  // Don't allow the mutex to be garbage collected when it falls out of scope.
  GC.KeepAlive(mutex);
}