Hi WPF is based on Direct3D, and is a bit different from win32 and forms which is based on GDI/GDI+.
In WPF you do this in your xaml(see example by maximus) or create your own window style.
There is a post here on how you should do this in WPF.
Another slightly related question.
A style :
<Style TargetType="Window" x:Key="TransparentWindowStyle">
<Setter Property="WindowStyle" Value="None"/>
<Setter Property="AllowsTransparency=" Value="True"/>
<Setter Property="Background" Value="Transparent"/>
</Style>
Skip the x:Key and it will be applied to all windows or you have to place in app.xaml or a place where it is shared, and apply it to the window. A bit overkill for just 3 properties, but handy if you are going to do other changes, that should be applied to multiple windows.
Hope it helps,
Stian