Copy value of field into the value of a different field
@Volker's tip gave me everything I needed and it's pretty simple as it turns out.

if (!empty($form_state['values']['some_other_field'])){
  $form['title']['#value'] = $form_state['values']['some_other_field'];
}


Set that in a hook_form_FORM_ID_alter and it works great.  The part I didn't have was the #value.