Q: How can I remove the 'You have already submitted this form. View your previous submissions' message from my webform?
A: There is no setting to get rid of this message, however it can be quite easily removed by overriding: theme_webform_view_messages() in your theme.

Here is a handy way of removing the (sometimes) annoying webforms message - 'You have already submitted this form. View your previous submissions', see comment #11 by kees@qrios, here:

http://drupal.org/node/321870

put the following code into your theme's template.php file (which you should find in your theme folder):

remembering to replace THEME with your theme name, and the flush your cache.

It worked a charm for us, thanks kees@qrios!