WordPress - List all posts gruped by category.

page-template.php

<?php

foreach ( get_categories( array( 'orderby' => 'name', 'order' => 'ASC' ) ) as $category ) {
    $posts = get_posts( array(
        'showposts' => -1,
        'category__in' => array( $category->term_id ),
        'ignore_sticky_posts' => 1
    ) );
    if ( $posts ) {
        echo '<h4>' . __( 'Categoria:' ) . ' <a href="' . get_category_link( $category->term_id ) . '">' . $category->name . '</a></h4>';
        foreach ( $posts as $post ) {
            setup_postdata( $post );
            echo '<p><a href="' . get_permalink() . '">' . get_the_title() . '</a></p>';
        }
    }
}