this.Cursor = Cursors.None;
There are several built in cursors such as a pen, cross, scroll, etc.
You can also use a custom cursor as follows:
this.Cursor = new Cursor("CustomCursorImage.jpg");
Because Cursor is a dependency property, it can also be used in XAML. Here are two examples on how to use custom cursors via XAML:
<Button Content="Wait" Cursor="Wait"/>