Unión implícita:
SELECT title, clean_title, body, published, name, slug
FROM posts, posts_tags, tags
WHERE posts.p_id=posts_tags.p_id AND posts_tags.t_id=tags.t_id
ORDER BY published DESC
Unión explícita:
SELECT title, clean_title, body, published, name, slug
FROM posts
LEFT JOIN posts_tags ON posts.p_id=posts_tags.p_id
LEFT JOIN tags ON posts_tags.t_id=tags.t_id
ORDER BY published DESC
Es refrescante ver un esquema de base de datos correcto y normalizado por una vez.