This article shows how to add a close button to the tabs on your TabControl.

Usage:
1. Add a new class to your application (preferably named TabControlEx.vb)
2. Copy and paste this code into that class.
3. Rebuild.
4. Now you should see a new item in the Control Toolbox named TabControlEx. Drag this control to your form.

Features:
1. The ShowCloseButtonOnTabs property controls whether close button is shown on the tabs on not. By default this is True.
2. The CloseButtonClick event is raised when any of the close buttons is clicked. By default this closes the tab, but you can set the e.Cancel = True inside this event handler to prevent closing the tab.

Code:
Option Strict On
Imports System.ComponentModel

<ToolboxBitmap(GetType(System.Windows.Forms.TabControl))> _
Public Class TabControlEx
   Inherits TabControl

   Private Declare Auto Function SetParent Lib "user32" (ByVal hWndChild As IntPtr, ByVal hWndNewParent As IntPtr) As IntPtr
   Protected CloseButtonCollection As New Dictionary(Of Button, TabPage)
   Private _ShowCloseButtonOnTabs As Boolean = True

   <Browsable(True), DefaultValue(True), Category("Behavior"), Description("Indicates whether a close button should be shown on each TabPage")> _
   Public Property ShowCloseButtonOnTabs() As Boolean
       Get
           Return _ShowCloseButtonOnTabs
       End Get
       Set(ByVal value As Boolean)
           _ShowCloseButtonOnTabs = value
           For Each btn In CloseButtonCollection.Keys
               btn.Visible = _ShowCloseButtonOnTabs
           Next
           RePositionCloseButtons()
       End Set
   End Property

   Protected Overrides Sub OnCreateControl()
       MyBase.OnCreateControl()
       RePositionCloseButtons()
   End Sub

   Protected Overrides Sub OnControlAdded(ByVal e As System.Windows.Forms.ControlEventArgs)
       MyBase.OnControlAdded(e)
       Dim tp As TabPage = DirectCast(e.Control, TabPage)
       Dim rect As Rectangle = Me.GetTabRect(Me.TabPages.IndexOf(tp))
       Dim btn As Button = AddCloseButton(tp)
       btn.Size = New Size(rect.Height - 1, rect.Height - 1)
       btn.Location = New Point(rect.X + rect.Width - rect.Height - 1, rect.Y + 1)
       SetParent(btn.Handle, Me.Handle)
       AddHandler btn.Click, AddressOf OnCloseButtonClick
       CloseButtonCollection.Add(btn, tp)
   End Sub

   Protected Overrides Sub OnControlRemoved(ByVal e As System.Windows.Forms.ControlEventArgs)
       Dim btn As Button = CloseButtonOfTabPage(DirectCast(e.Control, TabPage))
       RemoveHandler btn.Click, AddressOf OnCloseButtonClick
       CloseButtonCollection.Remove(btn)
       SetParent(btn.Handle, Nothing)
       btn.Dispose()
       MyBase.OnControlRemoved(e)
   End Sub

   Protected Overrides Sub OnLayout(ByVal levent As System.Windows.Forms.LayoutEventArgs)
       MyBase.OnLayout(levent)
       RePositionCloseButtons()
   End Sub

   Public Event CloseButtonClick As CancelEventHandler
   Protected Overridable Sub OnCloseButtonClick(ByVal sender As Object, ByVal e As EventArgs)
       If Not DesignMode Then
           Dim btn As Button = DirectCast(sender, Button)
           Dim tp As TabPage = CloseButtonCollection(btn)
           Dim ee As New CancelEventArgs
           RaiseEvent CloseButtonClick(sender, ee)
           If Not ee.Cancel Then
               Me.TabPages.Remove(tp)
               RePositionCloseButtons()
           End If
       End If
   End Sub

   Protected Overridable Function AddCloseButton(ByVal tp As TabPage) As Button
       Dim closeButton As New Button
       With closeButton
           '' TODO: Give a good visual appearance to the Close button, maybe by assigning images etc.
           ''       Here I have not used images to keep things simple.
           .Text = "X"
           .FlatStyle = FlatStyle.Flat
           .BackColor = Color.FromKnownColor(KnownColor.ButtonFace)
           .ForeColor = Color.White
           .Font = New Font("Microsoft Sans Serif", 6, FontStyle.Bold)
       End With
       Return closeButton
   End Function

   Public Sub RePositionCloseButtons()
       For Each item In CloseButtonCollection
           RePositionCloseButtons(item.Value)
       Next
   End Sub

   Public Sub RePositionCloseButtons(ByVal tp As TabPage)
       Dim btn As Button = CloseButtonOfTabPage(tp)
       If btn IsNot Nothing Then
           Dim tpIndex As Integer = Me.TabPages.IndexOf(tp)
           If tpIndex >= 0 Then
               Dim rect As Rectangle = Me.GetTabRect(tpIndex)
               If Me.SelectedTab Is tp Then
                   btn.BackColor = Color.Red
                   btn.Size = New Size(rect.Height - 1, rect.Height - 1)
                   btn.Location = New Point(rect.X + rect.Width - rect.Height, rect.Y + 1)
               Else
                   btn.BackColor = Color.FromKnownColor(KnownColor.ButtonFace)
                   btn.Size = New Size(rect.Height - 3, rect.Height - 3)
                   btn.Location = New Point(rect.X + rect.Width - rect.Height - 1, rect.Y + 1)
               End If
               btn.Visible = ShowCloseButtonOnTabs
               btn.BringToFront()
           End If
       End If
   End Sub

   Protected Function CloseButtonOfTabPage(ByVal tp As TabPage) As Button
       Return (From item In CloseButtonCollection Where item.Value Is tp Select item.Key).FirstOrDefault
   End Function
End Class