Simple function to get the hour time zone offset:

function get_time_zone_offset( ) {
     var current_date = new Date( );
     var gmt_offset = current_date.getTimezoneOffset( ) / 60;
     return gmt_offset;
}

HTML snippet to show this in action:

<p>
Time Zone offset: <span id="offset"></span>
</p>

<script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.3.2/jquery.min.js"></script>

<script type="text/javascript">
function get_time_zone_offset( ) {
    var current_date = new Date( );
    var gmt_offset = current_date.getTimezoneOffset( ) / 60;
    return gmt_offset;
}

$('#offset').html( get_time_zone_offset( ) );
</script>

Blog post: http://josephscott.org/archives/2009/08/detecting-client-side-time-zone-offset-via-javascript/