Find duplicate rows with PostgreSQL

I see a couple of options for you.

For a quick way of doing it, use something like this (it assumes your ID column is not unique as you mention 234 multiple times above):

CREATE TABLE tmpPhotos AS SELECT DISTINCT * FROM Photos;
DROP TABLE Photos;
ALTER TABLE tmpPhotos RENAME TO Photos;

Here is the SQL Fiddle.

You will need to add your constraints back to the table if you have any.

If your ID column is unique, you could do something like to keep your lowest id:

DELETE FROM P1  
USING Photos P1, Photos P2
WHERE P1.id > P2.id
   AND P1.merchant_id = P2.merchant_id  
   AND P1.url = P2.url;  

And the Fiddle.

Here is my take on it.

select * from (
  SELECT id,
  ROW_NUMBER() OVER(PARTITION BY merchant_Id, url ORDER BY id asc) AS Row
  FROM Photos
) dups
where 
dups.Row > 1

Feel free to play with the order by to tailor the records you want to delete to your specification.

SQL Fiddle => http://sqlfiddle.com/#!15/d6941/1/0

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SQL Fiddle for Postgres 9.2 is no longer supported; updating SQL Fiddle to postgres 9.3

The second part of sgeddes's answer doesn't work on Postgres (the fiddle uses MySQL). Here is an updated version of his answer using Postgres: http://sqlfiddle.com/#!12/6b1a7/1

DELETE FROM Photos AS P1  
USING Photos AS P2
WHERE P1.id > P2.id
   AND P1.merchant_id = P2.merchant_id  
   AND P1.url = P2.url;