Mysql join query for multiple "tags" (many-to-many relationship) that matches ALL tags?

Use:

  SELECT * 
    FROM OBJECTS o
    JOIN OBJECTSTAGS ot ON ot.object_id = o.id
    JOIN TAGS t ON t.id = ot.tag_id
   WHERE t.name IN ('tag1','tag2')
GROUP BY o.id
  HAVING COUNT(DISTINCT t.name) = 2

You were missing the HAVING clause.

There's no need to LEFT JOIN if you want only rows where both tags exist.