Style every second widget?

Use the dynamic_sidebar_params filter. The following code adds classes to say whether the widget is odd or even, what index it is in the sidebar, and what sidebar it’s in.

Note: the str_replace("class=\"", "class=\"$class ", $before_widget); code below depends on your before_widget using double quotes — it probably should be done with a regular expression to handle single quotes as well. I just haven’t ever got around to it.

function my_filter_dynamic_sidebar_params($params){

    static $sidebar_widget_count = array();
    $sidebar_id = $params[0]["id"];
    if (! isset($sidebar_widget_count[$sidebar_id])){
        $sidebar_widget_count[$sidebar_id] = 0;
    }
    $before_widget = $params[0]['before_widget'];
    $class = $sidebar_widget_count[$sidebar_id] % 2 ? 
        "widget-odd" : "widget-even";
    $class .= " widget-index-" . $sidebar_widget_count[$sidebar_id];
    $class .= " widget-in-$sidebar_id";
    $before_widget = str_replace("class=\"", 
        "class=\"$class ", $before_widget);
    $params[0]['before_widget'] = $before_widget;
    $sidebar_widget_count[$sidebar_id]++;
    return $params;
}

add_filter("dynamic_sidebar_params", "my_filter_dynamic_sidebar_params");