Certo che lo è.

codice:
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">

<html>
<head>
<title>Untitled</title>
<script language="JavaScript" type="text/javascript">
<!--
function pippo() {
 oColl = document.getElementsByTagName('DIV');
 for (i=0;i<oColl.length;i++) {
  curObj = oColl.item(i);
	if (curObj.className == "mia_classe") {
	 alert(curObj.id);
	}
 }
}
//-->
</script>

</head>
<body onload="pippo()">
<div id="livello_1" class="mia_classe"><div> 

<div id="livello_2" class="mia_classe"><div> 

<div id="livello_3"><div> 

<div id="livello_4" class="mia_classe"><div> 

</body>
</html>