By default navigation on Backspace and Shift+Backspace is enabled. In order to disable navigation when user presses Backspace or Shift+Backspace use the following approach:

C#

using DotNetBrowser;
using DotNetBrowser.DOM;
using DotNetBrowser.Events;
using DotNetBrowser.WPF;
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Windows;

namespace DisableBackspaceSample
{
    class Program
    {
        public class WindowMain : Window
        {
            private WPFBrowserView browserView;

            public WindowMain()
            {
                Browser browser = BrowserFactory.Create();
                browserView = new WPFBrowserView(browser);

                browser.LoadHandler = new SampleLoadHandler();

                Content = browserView;

                Width = 1024;
                Height = 768;
                this.Loaded += WindowMain_Loaded;
            }

            void WindowMain_Loaded(object sender, RoutedEventArgs e)
            {
                browserView.Browser.LoadURL("http://teamdev.com");
            }

            [STAThread]
            public static void Main()
            {
                Application app = new Application();

                WindowMain wnd = new WindowMain();
                app.Run(wnd);

                var browser = wnd.browserView.Browser;
                wnd.browserView.Dispose();
                browser.Dispose();
            }

            private class SampleLoadHandler : DefaultLoadHandler
            {
                public override bool CanNavigateOnBackspace()
                {
                    return false;
                }
            }
        }
    }
}

VB.NET

Imports DotNetBrowser
Imports DotNetBrowser.WPF
Imports System.Windows

Namespace DisableBackspaceSample
    Class Program
        Public Class WindowMain
            Inherits Window

            Private browserView As WPFBrowserView

            Public Sub New()
                Dim browser As Browser = BrowserFactory.Create()
                browserView = New WPFBrowserView(browser)
                browser.LoadHandler = New SampleLoadHandler()
                Content = browserView
                Width = 1024
                Height = 768
                AddHandler Me.Loaded, AddressOf WindowMain_Loaded
            End Sub

            Private Sub WindowMain_Loaded(ByVal sender As Object, ByVal e As RoutedEventArgs)
                browserView.Browser.LoadURL("http://teamdev.com")
            End Sub

            <STAThread>
            Public Shared Sub Main()
                Dim app As Application = New Application()
                Dim wnd As WindowMain = New WindowMain()
                app.Run(wnd)
                Dim browser = wnd.browserView.Browser
                wnd.browserView.Dispose()
                browser.Dispose()
            End Sub

            Private Class SampleLoadHandler
                Inherits DefaultLoadHandler

                Public Overrides Function CanNavigateOnBackspace() As Boolean
                    Return False
                End Function
            End Class
        End Class
    End Class
End Namespace