Ordenar itens com tags correspondentes pelo número de tags correspondentes

Tente algo assim:

select article_id, count(tag_id) as common_tag_count
from articles_tags 
group by tag_id
where tag_id in (
    select tag_id from articles_tags where article_id = 2
) and article_id != 2
order by common_tag_count desc;

A sintaxe pode precisar de alguns ajustes para o MySQL.

ou este que realmente funciona:;-)

SELECT at1.article_id, Count(at1.tag_id) AS common_tag_count
FROM articles_tags AS at1 INNER JOIN articles_tags AS at2 ON at1.tag_id = at2.tag_id
WHERE at2.article_id = 2
GROUP BY at1.article_id
HAVING at1.article_id != 2
ORDER BY Count(at1.tag_id) DESC;