Disable displaying user picture in page--user.tpl.php I don't want to display the user picture on the user account page. It is not a field, so I can't simply hide it in display settings. How can I disable it in Drupal 7?
If you don't want it at all in the user registration you can navigate to : admin/config/people/accounts/settings and uncheck "Enable user pictures" on that page. 

If you dont want it only on the user profile page you can add this snippet to template.php in your theme folder

function THEME-NAME_preprocess_page(&amp;$variables){
  if (arg(0)=="user" || arg(0)=="users" ){
    unset ($variables['page']['content']['system_main']['user_picture']);
  }
}