Pagination on category.php and tag.php not working

If you merely want to modify posts_per_page for tag and category archive index pages, don’t use query_posts(); instead, filter the $query via pre_get_posts:

function wpse87489_filter_pre_get_posts( $query ) {
    if ( ( is_category() || is_tag() ) && $query->is_main_query ) {
        $query->set( 'posts_per_page', '2' );
    }
}
add_action( 'pre_get_posts', 'wpse87489_filter_pre_get_posts' );