LEFT OUTER JOIN without using LEFT OUTER JOIN

We've been getting a number of this type of question lately: short, and simple on the surface. Short questions are wonderful, because they leave more room for the answer. Simple questions are even better, as long as they aren't too simple.

In this case, the question is not too simple, but I have difficulty imagining the circumstances which would lead to this requirement.

Here's the LEFT OUTER JOIN way to do it:

select A.foo
     , A.bar
     , B.qux
  from table1 as A
left outer
  join table2 as B
    on B.Aid = A.id

As you know, a LEFT OUTER JOIN returns all rows from the left table, with matching rows from the right table, if any. This is the same as an INNER JOIN combined in a UNION with a query on the left table only, with a NOT EXISTS subquery:

select A.foo
     , A.bar
     , B.qux
  from table1 as A
inner
  join table2 as B
    on B.Aid = A.id
union all
select A.foo
     , A.bar
     , null
  from table1 as A
 where not exists
       ( select *
           from table2 
          where Aid = A.id )

As mentioned, it's pretty hard to imagine why you wouldn't want to use the LEFT OUTER JOIN.