I wanted to do the same thing so I created an iframe in my html file –
<iframe src="headlines.php" name="blog" width="170" scrolling="no" frameborder="0" ><a href="http://www.yourdomain.com/headlines.php" title="whatever u want"></a></iframe>
Then created a php page, added the following code and titled it ‘headlines.php’
<?php
$how_many=4; //How many posts do you want to show
require_once("wordpress/wp-config.php"); // Change this for your path to wp-config.php file ?>
<?
$news=$wpdb->get_results("SELECT ID,post_title FROM $wpdb->posts
WHERE post_status= \"publish\" ORDER BY 'ID' DESC LIMIT ".$how_many);
foreach($news as $np){
printf ("
<li><a>%s</a></li>
", $np->ID,$np->post_title);
}?>
