Adding 'serial' to existing column in Postgres

TL;DR

Here's a version where you don't need a human to read a value and type it out themselves.

CREATE SEQUENCE foo_a_seq OWNED BY foo.a;
SELECT setval('foo_a_seq', coalesce(max(a), 0) + 1, false) FROM foo;
ALTER TABLE foo ALTER COLUMN a SET DEFAULT nextval('foo_a_seq'); 

Another option would be to employ the reusable Function shared at the end of this answer.

---

A non-interactive solution

Just adding to the other two answers, for those of us who need to have these Sequences created by a non-interactive script, while patching a live-ish DB for instance.

That is, when you don't wanna SELECT the value manually and type it yourself into a subsequent CREATE statement.

In short, you can not do:

CREATE SEQUENCE foo_a_seq
    START WITH ( SELECT max(a) + 1 FROM foo );

... since the START [WITH] clause in CREATE SEQUENCE expects a value, not a subquery.

Note: As a rule of thumb, that applies to all non-CRUD (i.e.: anything other than INSERT, SELECT, UPDATE, DELETE) statements in pgSQL AFAIK.

However, setval() does! Thus, the following is absolutely fine:

SELECT setval('foo_a_seq', max(a)) FROM foo;

If there's no data and you don't (want to) know about it, use coalesce() to set the default value:

SELECT setval('foo_a_seq', coalesce(max(a), 0)) FROM foo;
--                         ^      ^         ^
--                       defaults to:       0

However, having the current sequence value set to 0 is clumsy, if not illegal.
Using the three-parameter form of setval would be more appropriate:

--                                             vvv
SELECT setval('foo_a_seq', coalesce(max(a), 0) + 1, false) FROM foo;
--                                                  ^   ^
--                                                is_called

Setting the optional third parameter of setval to false will prevent the next nextval from advancing the sequence before returning a value, and thus:

the next nextval will return exactly the specified value, and sequence advancement commences with the following nextval.

— from this entry in the documentation

On an unrelated note, you also can specify the column owning the Sequence directly with CREATE, you don't have to alter it later:

CREATE SEQUENCE foo_a_seq OWNED BY foo.a;

In summary:

CREATE SEQUENCE foo_a_seq OWNED BY foo.a;
SELECT setval('foo_a_seq', coalesce(max(a), 0) + 1, false) FROM foo;
ALTER TABLE foo ALTER COLUMN a SET DEFAULT nextval('foo_a_seq'); 

---

Using a Function

Alternatively, if you're planning on doing this for multiple columns, you could opt for using an actual Function.

CREATE OR REPLACE FUNCTION make_into_serial(table_name TEXT, column_name TEXT) RETURNS INTEGER AS $$
DECLARE
    start_with INTEGER;
    sequence_name TEXT;
BEGIN
    sequence_name := table_name || '_' || column_name || '_seq';
    EXECUTE 'SELECT coalesce(max(' || column_name || '), 0) + 1 FROM ' || table_name
            INTO start_with;
    EXECUTE 'CREATE SEQUENCE ' || sequence_name ||
            ' START WITH ' || start_with ||
            ' OWNED BY ' || table_name || '.' || column_name;
    EXECUTE 'ALTER TABLE ' || table_name || ' ALTER COLUMN ' || column_name ||
            ' SET DEFAULT nextVal(''' || sequence_name || ''')';
    RETURN start_with;
END;
$$ LANGUAGE plpgsql VOLATILE;

Use it like so:

INSERT INTO foo (data) VALUES ('asdf');
-- ERROR: null value in column "a" violates not-null constraint

SELECT make_into_serial('foo', 'a');
INSERT INTO foo (data) VALUES ('asdf');
-- OK: 1 row(s) affected

Working for me in PostgreSQL 12.

It converts my existing int column to a serial column.

CREATE SEQUENCE table_name_id_seq;
ALTER TABLE table_name ALTER COLUMN id SET DEFAULT nextval('table_name_id_seq');
ALTER TABLE table_name ALTER COLUMN id SET NOT NULL;
ALTER SEQUENCE table_name_id_seq OWNED BY table_name.id;  
SELECT setval('table_name_id_seq', (SELECT max(id) FROM table_name));

Look at the following commands (especially the commented block).

DROP TABLE foo;
DROP TABLE bar;

CREATE TABLE foo (a int, b text);
CREATE TABLE bar (a serial, b text);

INSERT INTO foo (a, b) SELECT i, 'foo ' || i::text FROM generate_series(1, 5) i;
INSERT INTO bar (b) SELECT 'bar ' || i::text FROM generate_series(1, 5) i;

-- blocks of commands to turn foo into bar
CREATE SEQUENCE foo_a_seq;
ALTER TABLE foo ALTER COLUMN a SET DEFAULT nextval('foo_a_seq');
ALTER TABLE foo ALTER COLUMN a SET NOT NULL;
ALTER SEQUENCE foo_a_seq OWNED BY foo.a;    -- 8.2 or later

SELECT MAX(a) FROM foo;
SELECT setval('foo_a_seq', 5);  -- replace 5 by SELECT MAX result

INSERT INTO foo (b) VALUES('teste');
INSERT INTO bar (b) VALUES('teste');

SELECT * FROM foo;
SELECT * FROM bar;

You can also use START WITH to start a sequence from a particular point, although setval accomplishes the same thing, as in Euler's answer, eg,

SELECT MAX(a) + 1 FROM foo;
CREATE SEQUENCE foo_a_seq START WITH 12345; -- replace 12345 with max above
ALTER TABLE foo ALTER COLUMN a SET DEFAULT nextval('foo_a_seq');