A friend asked how he could pull the three most recent WordPress posts from a particular category on a non-WordPress site. He has the ability to connect to the WordPress database. So here is the code you need to pull this off.

mysql_connect("localhost","username","password");
mysql_select_db("database");

// Change the category name to whatever category you want to use
$categoryName = 'Music';

$query = "SELECT post_title, guid
  FROM
    wp_posts,
    wp_terms,
    wp_term_taxonomy,
    wp_term_relationships
  WHERE
   wp_terms.name = '$categoryName' and
   wp_terms.term_id = wp_term_taxonomy.term_id and
   wp_term_relationships.term_taxonomy_id
      = wp_term_taxonomy.term_taxonomy_id and
   wp_term_relationships.term_taxonomy_id
      = wp_term_taxonomy.term_taxonomy_id and
   wp_term_relationships.object_id = wp_posts.ID
  ORDER BY post_date DESC LIMIT 3";

$q = mysql_query($query);
while ($row = mysql_fetch_assoc($q)) {
    echo "
";
    echo "{$row['post_title']}";
    echo "

";
}