Profile Completion e-mail to user in Drupal
Use Rules, I actually have the below working for an Intranet site I manage. 

ON - Choose your event, maybe "User has logged in"
IF - "Content Profile's field 'field_NAME' has value"
DO - "Send a mail to the user"

Replace the field_NAME with the field you would like to check, In the IF I just check for a NULL value on a required field.

return array( 0 =&gt; array('value' =&gt; ''), );