The Boomcity.Biz homepage uses the below code to grab posts from a standard Wordpress blog, hosted on the same site. Boomcity also uses Google's Feedburner to grab posts from the Blips and Ifs blog.

THIS GOES FIRST IN THE HEAD:

<?php
// Include Wordpress
define('WP_USE_THEMES', false);
require('../address/of/blogfolder/wp-blog-header.php');
query_posts('showposts=5');
?>

THIS GOES IN THE BODY WHERE YOU WANT THE POSTS TO APPEAR:

<?php while (have_posts()): the_post(); ?>
<h2><?php the_title(); ?> : <?php the_date(); ?></h2>
<p class="dailycontent"><?php the_content(); ?></p>
<?php endwhile; ?>

Save the file as .php (not .html), but since php is just fancy html you can add this code to any standard website. For more assistance use the links below.