SQL select data from more than one table
You second query is incorrect because you have the table field_data_field_group_category two times, so it would generates duplicates and there's a missing coma in your SELECT clause. If you want your column in the result without filtering it, just put it in the SELECT clause and that's it.

SELECT og.label AS title
  , og.gid AS gid
  , field_data_field_group_category.field_group_category_value AS cat 
FROM og
LEFT JOIN field_data_field_group_category 
  ON og.etid = field_data_field_group_category.entity_id
ORDER BY title ASC