remove post and categories/tags count from right now dashboard widget

There is no filter in PHP, so we have to use JavaScript:

add_action( 'admin_footer-index.php', 'wpse_82132_hide_rows' );

function wpse_82132_hide_rows()
{
    $rows = array (
    #   'posts',
    #   'pages',
        'cats', // meoww!
        'tags',
    #   'comments',
    #   'b_approved',
    #   'b-waiting',
    #   'b-spam',
    );
    $find = '.' . join( ',.', $rows );
    ?>
<script>
jQuery( function( $ ) {
    $("#dashboard_right_now").find('<?php echo $find; ?>').parent().addClass('hidden');
});
</script>
    <?php
}

Result

To remove the widget completely:

add_action( 'wp_dashboard_setup', 'wpse_82132_remove_rn_dashboard' );

function wpse_82132_remove_rn_dashboard()
{
    remove_meta_box( 'dashboard_right_now', 'dashboard', 'normal' );
}