Register form breaks after changing submit button value with jQuery
Based on what Clive said and your response regarding the Ajax stuff, I edited your code. I am assuming you only want to change the text of the button for display purposes.

(function ($) {
  $(function() {

    // Create a copy of the button
    $('#registersubmit').after('&lt;input id="new-submit" class="form-submit" value="Jetzt registrieren"&gt;');
    // Hide original
    $('#registersubmit').hide();
    // When copy  is clicked, "click" the original
    $('#new-submit').click(function(){
      $('#registersubmit').click();
    });
    // Your code with changed IDs
    $("#edit-field-registrierung-als-und").change(function() {
      if ( this.value == "2") {
        $("#new-submit").val("Kostenpflichtig registrieren");
      }
      else {
        $("#new-submit").val("Jetzt registrieren");
      }
    });
  });
}(jQuery));


Can't test it as you appear to have the code active right now, but it should work fine in this scenario.