Checking the value of the window's "WindowState" in a Trigger

Or if you want a control other than the window to respond to the WindowState property you can use a DataTrigger instead:

<DataTrigger Binding="{Binding WindowState, RelativeSource={RelativeSource AncestorType=Window}}" 
             Value="Normal">
   <Setter Property="Fill" Value="Green"/>
</DataTrigger>

Works like this:

<Window.Style>
    <Style TargetType="Window">
        <Style.Triggers>
            <Trigger Property="WindowState" Value="Minimized">
                <Setter Property="ShowInTaskbar" Value="False" />
            </Trigger>
        </Style.Triggers>
    </Style>
</Window.Style>

Edit: You need to place your trigger in the Window.Style.