The error message I got:
warning: Cannot modify header information - headers already sent by (output started at /home/{username}/public_html/drupal/sites/all/modules/{modulename}/{modulename}.module:1) in /home/{username}/public_html/drupal/includes/common.inc on line 148.
It took a while to figure out what the problem was. The first thing to say is that the line and file number it says is causing the problem usually is the file and line number causing the problem. So I opened up the custom module I'd written and here was what it had in the first two lines:
<?php
// $Id$
Nothing strange about that. And there was no white space preceding the opening of the php code tag.
To cut a very boring story short, the problem turned out to be that I'd saved the file as UTF-8 and before the opening tag the text-editor had stuck in an invisible UTF-8 marker character which was being sent to the browser before the headers and thus causing the error.
The solution is to change the text file to ASCII (or ANSI as some text-editors call it) or find another way to remove that preceding character(s?) and if any preceding characters show up in the ASCII file then delete them and save the file.