The code

Please note that I have created new WordPress template file and save it as ’sitemap.php’ in theme’s root folder. For more info regarding custom WP template files and how to use them, please refer to this page.
Also, another important info is that this code will work only for Custom Permalink structure set to /%category%/%postname%/.

<?php
    // easy job for pages...
    echo '<ul>';
    echo '<li><h1>PAGES:</h1></li>';
    echo '<li><ul>';
    wp_list_pages( 'title_li=&echo=1' );
    echo '</ul></li></ul>';

    // categories sitemap will be tough...get'em all
    $subcats = wp_list_categories( 'echo=0&use_desc_for_title=0&title_li=' );
    // anybody there?
    preg_match_all( '|<a.*?href=[\'"](.*?)[\'"].*?>|i', $subcats, $m );
	if( !$m[ 1 ] ) {
		// no categs, subcategs or whatsoever...
		echo "There are no categories added to your WordPress site.";
	} else {
		$arr_categories = array();
		$arr_orig_urls  = array();
		foreach( $m[ 1 ] as $key => $value ) {
			// $value will keep the URL, extract category slug
			$arr_of_url = explode( '/', $value );
			array_pop( $arr_of_url ); // remove empty
			// push the last
			array_push( $arr_categories, $arr_of_url[ count( $arr_of_url ) - 1 ] );
			// get its URL
			array_push( $arr_orig_urls, $value );
		}
	}

	if( count( $arr_categories ) > 0 ) {
		// now we have entire logical structure of all categories
		// let's try to get ID for each of these
		echo '<ul>';
		echo '<li><h1>CATEGORIES:</h1></li>';
		$i = 0;
		while( $i < count( $arr_categories ) ) {
			// shortcut by WP built-in
			$idObj = get_category_by_slug( $arr_categories[ $i ] );
			$catid = $idObj->term_id;

			// check whether this is root category. If true, make an outset in list, otherwise leave inset.
			if( $idObj->category_parent > 0 ) echo '<li><ul>';

			// get category real name and link
			$cat_real_name = $wpdb->get_var( "SELECT name FROM $wpdb->terms WHERE term_id=" . $catid );
			echo '<li><h2><a href="' . $arr_orig_urls[ $i ] . '">' . $cat_real_name . '</a></h2></li>';

			// generate list of posts
			echo '<li><ul>';
			query_posts( 'cat=' . $catid  . '&order=ASC' ); // change to DESC - if required
			while( have_posts() ) : the_post();
?>

<li><a href="<?php the_permalink(); ?>" title="<?php the_title(); ?>"><?php the_title(); ?></a></li>
<?php
			endwhile;
			echo '</ul></li>';
			if( $idObj->category_parent > 0 ) echo '</ul></li>';
			$i ++;
		}
	echo '</ul>';
	}
?>

Hopefully you will find this code useful. Any comment/suggestion regarding improvement is welcome!