excessive "access denied" logs? I've setup a Drupal site and had to turn off user registration because of the amount of bogus accounts being created. Now when I check the logs I see loads of access denied messages, usually for pages 
node/add
user/register


Is this normal for a drupal (possibly any) site, and something to be expected? 
It seems excessive to me, so I'd like to understand if this is a normal problem for websites, drupal or otherwise?
Yes, this is a common problem. A spam bot has crawled your site, realizes it's a Drupal site, and it going through its functions to spam content (e.g. user register &amp; node posting). This isn't exclusive to Drupal; there many kinds spam bot software that target specifics CMSes and any other comment/content submission forms.

You should look into various Drupal spam prevention modules like CAPTCHA, Botcha, etc.