MySQL seleccione unirse donde Y donde

Este tipo de problema se conoce como división relacional

SELECT Products.* 
FROM Products
JOIN ProductTags ON Products.id = ProductTags.product_id
WHERE ProductTags.tag_id IN (1,2,3)
GROUP BY Products.id /*<--This is OK in MySQL other RDBMSs 
                          would want the whole SELECT list*/

HAVING COUNT(DISTINCT ProductTags.tag_id) = 3 /*Assuming that there is a unique
                                              constraint on product_id,tag_id you 
                                              don't need the DISTINCT*/