Add a Custom Class to Admin Menus

The following does the job:

add_action( 'admin_init','wpse_60168_custom_menu_class' );

function wpse_60168_custom_menu_class() 
{
    global $menu;

    foreach( $menu as $key => $value )
    {
        if( 'Posts' == $value[0] )
            $menu[$key][4] .= " custom-class-1";

        if( 'Pages' == $value[0] )
            $menu[$key][4] .= " custom-class-2";
    }
}

And if you want to inspect what the $menu contains, use this:

add_action( 'admin_init','wpse_60168_var_dump_and_die' );

function wpse_60168_var_dump_and_die() 
{
    global $menu;   
    echo '<pre>' . print_r( $menu, true ) . '</pre>';
    wp_die();
}