What's the Fastest Way to Do a Bulk Insert into Postgres?

There is an alternative to using COPY, which is the multirow values syntax that Postgres supports. From the documentation:

INSERT INTO films (code, title, did, date_prod, kind) VALUES
    ('B6717', 'Tampopo', 110, '1985-02-10', 'Comedy'),
    ('HG120', 'The Dinner Game', 140, DEFAULT, 'Comedy');

The above code inserts two rows, but you can extend it arbitrarily, until you hit the maximum number of prepared statement tokens (it might be $999, but I'm not 100% sure about that). Sometimes one cannot use COPY, and this is a worthy replacement for those situations.

One way to speed things up is to explicitly perform multiple inserts or copy's within a transaction (say 1000). Postgres's default behavior is to commit after each statement, so by batching the commits, you can avoid some overhead. As the guide in Daniel's answer says, you may have to disable autocommit for this to work. Also note the comment at the bottom that suggests increasing the size of the wal_buffers to 16 MB may also help.

UNNEST function with arrays can be used along with multirow VALUES syntax. I'm think that this method is slower than using COPY but it is useful to me in work with psycopg and python (python list passed to cursor.execute becomes pg ARRAY):

INSERT INTO tablename (fieldname1, fieldname2, fieldname3)
VALUES (
    UNNEST(ARRAY[1, 2, 3]), 
    UNNEST(ARRAY[100, 200, 300]), 
    UNNEST(ARRAY['a', 'b', 'c'])
);

without VALUES using subselect with additional existance check:

INSERT INTO tablename (fieldname1, fieldname2, fieldname3)
SELECT * FROM (
    SELECT UNNEST(ARRAY[1, 2, 3]), 
           UNNEST(ARRAY[100, 200, 300]), 
           UNNEST(ARRAY['a', 'b', 'c'])
) AS temptable
WHERE NOT EXISTS (
    SELECT 1 FROM tablename tt
    WHERE tt.fieldname1=temptable.fieldname1
);

the same syntax to bulk updates:

UPDATE tablename
SET fieldname1=temptable.data
FROM (
    SELECT UNNEST(ARRAY[1,2]) AS id,
           UNNEST(ARRAY['a', 'b']) AS data
) AS temptable
WHERE tablename.id=temptable.id;

You can use COPY table TO ... WITH BINARY which is "somewhat faster than the text and CSV formats." Only do this if you have millions of rows to insert, and if you are comfortable with binary data.

Here is an example recipe in Python, using psycopg2 with binary input.

      ((this is a WIKI you can edit and enhance the answer!))

The external file is the best and typical bulk-data

The term "bulk data" is related to "a lot of data", so it is natural to use original raw data, with no need to transform it into SQL. Typical raw data files for "bulk insert" are CSV and JSON formats.