Build JSON object from one-to-many relationship data in a single query?

If containers can be empty, the currently accepted solution does not work for you. It has to be an outer join to preserve rows without match - to get equivalent results to the correlated subqueries you are using in your fiddle:

select *, array(select thing_id from container_thing where container_id = container.id) as "thingIds"
from container

1.

SELECT to_json(sub) AS container_with_things
FROM  (
   SELECT c.*, json_agg(thing_id) AS "thingIds"
   FROM   container c
   LEFT   JOIN container_thing ct ON  ct.container_id = c.id
   WHERE  c.id IN (<list of container ids>)
   GROUP  BY c.id
   ) sub;

2.

With more than a few rows per container (you mentioned 20) it's typically faster to aggregate before you join:

SELECT to_json(sub) AS container_with_things
FROM  (
   SELECT c.*, ct."thingIds"
   FROM   container c
   LEFT   JOIN (
      SELECT container_id AS id, json_agg(thing_id) AS "thingIds"
      FROM   container_thing
      WHERE  container_id IN (<list of container ids>) -- repeat condition
      GROUP  BY 1
      ) ct USING (id)
   WHERE  c.id IN (<list of container ids>)
   ) sub;

3.

Or you can combine the ARRAY constructor you found with LEFT JOIN LATERAL:

SELECT to_json(sub) AS container_with_things
FROM  (
   SELECT c.*, ct."thingIds"
   FROM   container c
   LEFT   JOIN LATERAL (
      SELECT ARRAY (
         SELECT thing_id
         FROM   container_thing
         WHERE  container_id = c.id
         -- ORDER  BY thing_id  -- optional order for deterministic results
         ) AS "thingIds"
      ) ct ON true
   WHERE  c.id IN (<list of container ids>)
   ) sub;

• What is the difference between LATERAL and a subquery in PostgreSQL?

Might be faster, yet.

SQL Fiddle. (Extending @a_horse's fiddle.)

Note that the result for empty containers is subtly different in the three queries above:

1. "thingIds":[null]
2. "thingIds":null
3. "thingIds":[]

4.

In Postgres 9.5 (since you are using it) you could also work with jsonb and its functionality and one less subquery:

SELECT jsonb_set(to_jsonb(c), '{thingIds}', "thingIds") AS container_with_things
FROM   container c
LEFT   JOIN (
   SELECT container_id AS id, jsonb_agg(thing_id) AS "thingIds"
   FROM   container_thing
   WHERE  container_id IN (<list of container ids>) -- repeat condition
   GROUP  BY 1
   ) ct USING (id)
WHERE  c.id IN (<list of container ids>);

Alternatively:

SELECT to_jsonb(c) || jsonb_build_object('thingIds', "thingIds") AS container_with_things
FROM   ... 

This looks like a good fit for Postgres' JSON functions:

select to_json(x)
from (
  select c.*, json_agg(ct.thing_id) as "thingIds"
  from container_thing ct
    join container c on ct.container_id = c.id
  group by c.id
) x

SQLFiddle example: http://sqlfiddle.com/#!15/cd9992/1