torrius,
или так
<!DOCTYPE HTML>
<html>
<head>
<meta charset="utf-8">
<script type="text/javascript">
function addInput(){
document.getElementById("add_block").insertAdjacentHTML("beforeEnd", "<br/><input type='text' />");
}
</script>
</head>
<body>
<div id="add_block">
<input type="text" />
</div>
<span onclick="addInput()" style="cursor: pointer;">add</span>
</body>
</html>