I was assuming that if I didn't do this, the main thread would just
suck all of the processor iterating through the while loop; I guess now
that isn't correct? Sorry, I've been teaching myself on the fly, no
formal programming education (I'm sure it shows)!
The below code works.

Question: On the main form code "SetText" routine, should I uncomment
the Monitor.Enter(me) & Monitor.Exit(me) when I have more than one
background thread running at the same time, updating the textbox?

What I've done so far is this. Main form code follows:
Imports System.Threading
Public Delegate Sub SetTextCallback(ByVal [text] As String)

Public Class Form1
   Dim tClass As count
   Dim t As Thread
   Private Sub btnStart_Click(ByVal sender As System.Object, ByVal e
As System.EventArgs) Handles btnStart.Click
       btnStart.Enabled = False
       tClass = New count
       t = New Thread(AddressOf tClass.bProcess)
       t.Start()
       btnStart.Enabled = True
   End Sub
   Public Sub SetText(ByVal [text] As String)
       ' InvokeRequired required compares the thread ID of the
       ' calling thread to the thread ID of the creating thread.
       ' If these threads are different, it returns true.
       'Monitor.Enter(Me)
       If Me.txtOutput.InvokeRequired Then
           Dim d As New SetTextCallback(AddressOf SetText)
           Me.Invoke(d, New Object() {[text]})
       Else
       Me.txtOutput.Text = [text] & txtOutput.Text
           Me.txtOutput.Refresh()
       End If
       'Monitor.Exit(Me)
   End Sub
   Private Sub btnAbort_Click(ByVal sender As System.Object, ByVal e
As System.EventArgs) Handles btnAbort.Click
       t.Abort()
   End Sub

End Class

And in the "Count" class code, I've put this:

Imports system.threading

Public Class count
   Public i As Integer
   Dim f1 As Form1
   Dim st As SetTextCallback
   Sub New()
       i = 0
       st = New SetTextCallback(AddressOf Form1.SetText)
   End Sub
   Sub bProcess()
       For i = 1 To 1000
           st(i.ToString & " ")
           Thread.Sleep(10)
       Next
   End Sub
End Class