Me pareceio interesante tu duda me puse a buscar y encontre esto, espero y te sirva...
Código HTML:
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title>jQuery Scroller</title>
<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.3.2/jquery.min.js"></script>
</head>
<body>
<div id="myDiv" style="width: 500px; height: 100px; overflow: auto; border: 1px solid black;"></div>
<input type="text" id="myTextInput" />
<input type="button" value="Send" id="postButton" />
<div id="info"/>
<script type="text/javascript">
$(document).ready(function(){
$('#postButton').click(function(){
$('#myDiv').append($('#myTextInput').val() + '<br/>');
$('#myTextInput').val('');
$("#myDiv").animate({ scrollTop: $("#myDiv").attr("scrollHeight") - $('#myDiv').height() }, 3000);
});
});
</script>
</body>
</html>