PHP:cómo actualizar datos a MySQL al hacer clic en un botón de radio

Algo para ponerte en un camino más bonito:

  // $_POST is way cooler than $_REQUEST
  if (isset($_POST['gender']) && !empty($_POST['gender'])) {

      // sql injection sucks
      $gender = my_real_escape_string($_POST['gender']);

      // cast it as an integer, sql inject impossible
      $id = intval($_GET['id']);

      if($id) {
          // spit out the boolean INSERT result for use by client side JS
          if(mysql_query("UPDATE users SET gender=$gender WHERE id=$id")) {
              echo '1';
              exit;
          } else {
              echo '0';
              exit;
          }
      }
  }

Asumiendo el mismo marcado, una solución ajaxy (usando jQuery ):

<script>
var id = <?=$id?>;

// when the DOM is ready
$(document).ready(function() {

    // 'click' because IE likes to choke on 'change'
    $('input[name=gender]').click(function(e) {

        // prevent normal, boring, tedious form submission
        e.preventDefault();

        // send it to the server out-of-band with XHR
        $.post('save.php?id=' + id, function() {
            data: $(this).val(),
            success: function(resp) { 
                if(resp == '1') {
                    alert('Saved successfully');
                } else {
                    alert('Oops, something went wrong!');
                }
            }
        });
    });
});
</script>