Så här kanske:
<script type="text/javascript">
<!--
function writeToTextarea(v){
document.forms["form"].elements["textarea"].value = v;
};
//-->
</script>
<body>
<form name="form">
<input type="text" onkeyup="writeToTextarea(this.value)">
<textarea name="textarea" rows="10" cols="30"></textarea>
</form>
</body>
