WPF Command Line

First, find this attribute at the top of your App.xaml file and remove it:

StartupUri="Window1.xaml"

That means that the application won't automatically instantiate your main window and show it.

Next, override the OnStartup method in your App class to perform the logic:

protected override void OnStartup(StartupEventArgs e)
{
    base.OnStartup(e);

    if ( /* test command-line params */ )
    {
        /* do stuff without a GUI */
    }
    else
    {
        new Window1().ShowDialog();
    }
    this.Shutdown();
}

To check for the existence of your argument - in Matt's solution use this for your test:

e.Args.Contains("MyTriggerArg")

A combination of the above solutions, for .NET 4.0+ with output to the console:

[DllImport("Kernel32.dll")]
public static extern bool AttachConsole(int processID);

protected override void OnStartup(StartupEventArgs e)
{
    base.OnStartup(e);

    if (e.Args.Contains("--GUI"))
    {
        // Launch GUI and pass arguments in case you want to use them.
        new MainWindow(e).ShowDialog();
    }
    else
    {
        //Do command line stuff
        if (e.Args.Length > 0)
        {
            string parameter = e.Args[0].ToString();
            WriteToConsole(parameter);
        }
    }
    Shutdown();
}

public void WriteToConsole(string message)
{
    AttachConsole(-1);
    Console.WriteLine(message);
}

Alter the constructor in your MainWindow to accept arguments:

public partial class MainWindow : Window
{
    public MainWindow(StartupEventArgs e)
    {
        InitializeComponent();
    }
}

And don't forget to remove:

StartupUri="MainWindow.xaml"