Query to get all rows from previous month

SELECT * FROM table
WHERE YEAR(date_created) = YEAR(CURRENT_DATE - INTERVAL 1 MONTH)
AND MONTH(date_created) = MONTH(CURRENT_DATE - INTERVAL 1 MONTH)

If there are no future dates ...

SELECT * 
FROM   table_name 
WHERE  date_created > (NOW() - INTERVAL 1 MONTH);

Tested.

Alternatively to hobodave's answer

SELECT * FROM table
WHERE YEAR(date_created) = YEAR(CURRENT_DATE - INTERVAL 1 MONTH)
AND MONTH(date_created) = MONTH(CURRENT_DATE - INTERVAL 1 MONTH)

You could achieve the same with EXTRACT, using YEAR_MONTH as unit, thus you wouldn't need the AND, like so:

SELECT * FROM table
WHERE EXTRACT(YEAR_MONTH FROM date_created) = EXTRACT(YEAR_MONTH FROM CURDATE() - INTERVAL
1 MONTH)

Here's another alternative. Assuming you have an indexed DATE or DATETIME type field, this should use the index as the formatted dates will be type converted before the index is used. You should then see a range query rather than an index query when viewed with EXPLAIN.

SELECT
    * 
FROM
    table
WHERE 
    date_created >= DATE_FORMAT( CURRENT_DATE - INTERVAL 1 MONTH, '%Y/%m/01' ) 
AND
    date_created < DATE_FORMAT( CURRENT_DATE, '%Y/%m/01' )