I’ve just begun upgrading a Drupal 6 custom theme to Drupal 7. And after a couple of attempts at cleaning up my theme (ok, numerous attempts), things started to render correctly.
However, I did notice that the taxonomy terms that I had removed from node.tpl.php in my Drupal 6 theme were now appearing in 7. After some investigation, I did notice that while logged in as admin, under Structure > Content Types > then manage display for the respective content type you could make certain Fields hidden.
While it took me a little bit of adjustment to find at first, this is great. I just set the Label and Format to field I didn’t want to display on my Page to <hidden> and all is well again.