EDIT:
If you're saying that you're changing it from a nested element, you don't need the ID at all. You can do this instead:
$(this).closest('td').toggleClass('change_me some_other_class');
//or
$(this).parents('td:first').toggleClass('change_me some_other_class');
Original answer:
$('#td_id').removeClass('change_me').addClass('some_other_class');
Another option is:
$('#td_id').toggleClass('change_me some_other_class');