The RichTextBox control is very versatile, but I don't think that it is able
to show whitespace (tabs and space characters).
Only manually converting the space characters to the dot character
(ALT+0183) comes into mind. Of course, this solution is far from perfect,
but should work nonetheless. Third party component will most probably help
you here.
Oh, in case you are interested, there are two nice RichTextBox customization
related articles written by Pete Vidler: