I found a great tutorial on how to password protect WordPress at this site. Just folow the steps below:

  1. Go to Users ? Authors & Users sub-panel.
  2. Add a new user in the Add New User section. This login will be used to access your WordPress by other user. Or go to Settings ? General ? Membership and check “Anyone can register”.
  3. Add the following lines to your Theme’s template functions.php file (For example, functions.php file for a Theme named “default” would probably reside in the directory wp-content/themes/default/functions.php) or create it as a Plugin by filling the additional Standard Plugin Information:
    function password_protected() {
    	if ( !is_user_logged_in() ) {
    		auth_redirect();
      }
    }
    
    add_action('template_redirect', 'password_protected');
    add_action('do_feed', 'password_protected');
  4. Go to Settings ? Discussion sub-panel. Under Default article settings, uncheck “Attempt to notify any blogs linked to from the article (slows down posting.)”.
  5. Finally, go to Settings ? Privacy and set “Blog Visibility to I would like to block search engines, but allow normal visitors”. Click Save Changes.

Now visitors will be asked to log in using WordPress login form to view your WordPress blog / site. This is very suitable for someone that wanted privacy or owned a private WordPress blog / site.