You could create a container div for all of the clones and just keep appending new elements to this.
HTML Code:
<!DOCTYPE html>
<html>
<head>
<title>Title</title>
<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.7.2/jquery.min.js" type="text/javascript"></script>
</head>
<body>
<div id="master">
<div><input type="text"><a href="#" class="add-but"><img src="img/add.png" width="16" height="16"></a></div>
</div>
<div class="clones"></div>
<script>
$(document).ready(function() {
$(".add-but").live('click', function () {
$(".clones").append($("#master").html());
});
});
</script>
</body>
</html>
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