WP - List all Categories and Posts

<?php
/* template name: Posts by Category! */
get_header(); ?>

        <div id="container">
            <div id="content" role="main">

            <?php
            // get all the categories from the database
            $cats = get_categories();

                // loop through the categries
                foreach ($cats as $cat) {
                    // setup the cateogory ID
                    $cat_id= $cat->term_id;
                    // Make a header for the cateogry
                    echo "<h2>".$cat->name."</h2>";
                    // create a custom wordpress query
                    query_posts("cat=$cat_id&post_per_page=100");
                    // start the wordpress loop!
                    if (have_posts()) : while (have_posts()) : the_post(); ?>

                        <?php // create our link now that the post is setup ?>
                        <a href="<?php the_permalink();?>"><?php the_title(); ?></a>
                        <?php echo '<hr/>'; ?>

                    <?php endwhile; endif; // done our wordpress loop. Will start again for each category ?>
                <?php } // done the foreach statement ?>

            </div><!-- #content -->
        </div><!-- #container -->

<?php get_sidebar(); ?>
<?php get_footer(); ?>