What is the best way to stop a user from resizing the top-level window of an application written in WPF?

You will want to use the ResizeMode.NoResize on the window.

<Window x:Class="WpfApplication5.Window1"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    ResizeMode="NoResize">
</Window>

A WPF quirk to note is that if ResizeMode="NoResize" and WindowStyle="None" you will lose the chrome around the entirely in Vista Aero.