You can specify the visibility of the scrollbar for both vertical and horizontal scrolling to four options, using the ScrollViewer.HorizontalScrollBarVisibility and ScrollViewer.VerticalScrollBarVisibility attached properties: Auto, Disabled, Hidden and Visible.
<ListView ScrollViewer.HorizontalScrollBarVisibility="Disabled">
Disabled will have it never show up and scrolling is not possible, Hidden will have it not show, but will allow users to scroll using text selection and arrow keys/mousewheel, etc.