You may want to try something like the following (tested in MySQL, but I guess it should be easy to port to Postgres):
SELECT l.id, l.timestamp, l.value
FROM log l
INNER JOIN (
SELECT MIN(timestamp) first_timestamp
FROM log
GROUP BY DATE(timestamp)
) sub_l ON (sub_l.first_timestamp = l.timestamp)
WHERE l.timestamp > DATE_ADD(NOW(), INTERVAL -30 DAY);
Note that this assumes that your timestamps are unique.
Test Case (in MySQL):
CREATE TABLE log (id int, timestamp datetime, value int);
INSERT INTO log VALUES (1, '2010-06-01 02:00:00', 100);
INSERT INTO log VALUES (2, '2010-06-01 03:00:00', 200);
INSERT INTO log VALUES (3, '2010-06-01 04:00:00', 300);
INSERT INTO log VALUES (4, '2010-06-02 02:00:00', 400);
INSERT INTO log VALUES (5, '2010-06-02 03:00:00', 500);
INSERT INTO log VALUES (6, '2010-06-03 02:00:00', 600);
INSERT INTO log VALUES (7, '2010-06-04 02:00:00', 700);
INSERT INTO log VALUES (8, '2010-06-04 03:00:00', 800);
INSERT INTO log VALUES (9, '2010-06-05 05:00:00', 900);
INSERT INTO log VALUES (10, '2010-06-05 03:00:00', 1000);
Result:
+------+---------------------+-------+
| id | timestamp | value |
+------+---------------------+-------+
| 1 | 2010-06-01 02:00:00 | 100 |
| 4 | 2010-06-02 02:00:00 | 400 |
| 6 | 2010-06-03 02:00:00 | 600 |
| 7 | 2010-06-04 02:00:00 | 700 |
| 10 | 2010-06-05 03:00:00 | 1000 |
+------+---------------------+-------+
5 rows in set (0.00 sec)