Theming the user registration form
It turns out that I need a combination of changes:

I had to implement hook_form_alter()in a module and set the form's #theme property:

function mymodule_form_user_register_form_alter(&amp;$form, &amp;$form_state, $form_id) {
  $form['#theme'] = 'user_register';
}


And then in template.php:

function mytheme_theme($existing, $type, $theme, $path){
  return array(
    'user_register' =&gt; array(
      'render element' =&gt; 'form',
      'template' =&gt; 'templates/user-register',
    ),
  );
}

function mytheme_preprocess_user_register(&amp;$variables) {
  $variables['rendered'] = drupal_render_children($variables['form']);
}


And then I added user-register.tpl.php with my desired markup, and 

&lt;?php echo $rendered; ?&gt; 


to print the form.