[danik.js]

<select name="select">
<option value="1">1</option>
<option value="2">2</option>
<option value="3">3</option>
</select>
<script src="//code.jquery.com/jquery-latest.js"></script>
<script>
    if (localStorage.option !== undefined) {
        $('select[name="select"]').prop('selectedIndex', localStorage.option);
    }
    $('select[name="select"]').change(function(){
        localStorage.option = this.selectedIndex;
    });
</script>