If you're trying to do this in your own custom module in Drupal 7:
$_REQUEST['destination'] = 'anywhere_you_want_to_go_to';
hook_form_user_register_form_alter() always runs on the registration form. Change mymodulename to your module and make sure it's on.
The second line is the line that redirects on submit (if it validates). I don't know of any way to not redirect, but you can redirect to the page you're redirecting away from for the same result. Change the "anywhere_you_want_to_go_to" string to the page you want to go to. eg. "user/register" or "<front>".