event.preventDefault()を使用する

$('#formId').submit(function (e) {
    if ($('#assettype').val() == '') {
    e.preventDefault(); //stop form submission
}
});

jQuery バリデーターの使用

$.validator.addMethod('notNone', function (value, element) {
    return (value != '');
}, 'Please select an option');
$("form").validate({
    rules: {
        assettype: {
            required: true,
            notNone: true
        }
    }
});

<form id="my_form" method="POST" action="" >
<select id="assettype" name="assettype" class="input-medium required">
  <option value="0" >-- Please select --</option>
  <option value="1">Printer</option>
  <option value="2">Scanner</option>
</select>
</form>
<script type="text/javascript">
  $("#my_form").submit(
    var check_value = $("#assettype").val();
    if (check_value == 0)
    {
      e.preventDefault();
      // prevent the user he has to choose something
      // by an alert for example, or background change of the element
      $("#assettype").css("background-color", "red");
      return false;
    }
    else
    {
      // and restore it if it's ok
      $("#assettype").css("background-color", "inherit");
    }
    return true;
  });
</script>