Find highest level of a hierarchical field: with vs without CTEs
You definitely have to script this via MySQL Stored Procedure Language

Here is a Stored Function called GetParentIDByIDto Retrieve a ParentID given an ID to Search For

DELIMITER $$
DROP FUNCTION IF EXISTS `junk`.`GetParentIDByID` $$
CREATE FUNCTION `junk`.`GetParentIDByID` (GivenID INT) RETURNS INT
DETERMINISTIC
BEGIN
    DECLARE rv INT;

    SELECT IFNULL(parent_id,-1) INTO rv FROM
    (SELECT parent_id FROM pctable WHERE id = GivenID) A;
    RETURN rv;
END $$
DELIMITER ;


Here is a Stored Function called GetAncestryto Retrieve a List of ParentIDs starting from the First Generation all the up the hierarchy given an ID to start with:

DELIMITER $$
DROP FUNCTION IF EXISTS `junk`.`GetAncestry` $$
CREATE FUNCTION `junk`.`GetAncestry` (GivenID INT) RETURNS VARCHAR(1024)
DETERMINISTIC
BEGIN
    DECLARE rv VARCHAR(1024);
    DECLARE cm CHAR(1);
    DECLARE ch INT;

    SET rv = '';
    SET cm = '';
    SET ch = GivenID;
    WHILE ch &gt; 0 DO
        SELECT IFNULL(parent_id,-1) INTO ch FROM
        (SELECT parent_id FROM pctable WHERE id = ch) A;
        IF ch &gt; 0 THEN
            SET rv = CONCAT(rv,cm,ch);
            SET cm = ',';
        END IF;
    END WHILE;
    RETURN rv;
END $$
DELIMITER ;


Here is something to generate sample data:

USE junk
DROP TABLE IF EXISTS pctable;
CREATE TABLE pctable
(
    id INT NOT NULL AUTO_INCREMENT,
    parent_id INT,
    PRIMARY KEY (id)
) ENGINE=MyISAM;
INSERT INTO pctable (parent_id) VALUES (0);
INSERT INTO pctable (parent_id) SELECT parent_id+1 FROM pctable;
INSERT INTO pctable (parent_id) SELECT parent_id+2 FROM pctable;
INSERT INTO pctable (parent_id) SELECT parent_id+3 FROM pctable;
INSERT INTO pctable (parent_id) SELECT parent_id+4 FROM pctable;
INSERT INTO pctable (parent_id) SELECT parent_id+5 FROM pctable;
SELECT * FROM pctable;


Here is what it generates:

mysql&gt; USE junk
Database changed
mysql&gt; DROP TABLE IF EXISTS pctable;
Query OK, 0 rows affected (0.00 sec)

mysql&gt; CREATE TABLE pctable
    -&gt; (
    -&gt;     id INT NOT NULL AUTO_INCREMENT,
    -&gt;     parent_id INT,
    -&gt;     PRIMARY KEY (id)
    -&gt; ) ENGINE=MyISAM;
Query OK, 0 rows affected (0.05 sec)

mysql&gt; INSERT INTO pctable (parent_id) VALUES (0);
Query OK, 1 row affected (0.00 sec)

mysql&gt; INSERT INTO pctable (parent_id) SELECT parent_id+1 FROM pctable;
Query OK, 1 row affected (0.00 sec)
Records: 1  Duplicates: 0  Warnings: 0

mysql&gt; INSERT INTO pctable (parent_id) SELECT parent_id+2 FROM pctable;
Query OK, 2 rows affected (0.00 sec)
Records: 2  Duplicates: 0  Warnings: 0

mysql&gt; INSERT INTO pctable (parent_id) SELECT parent_id+3 FROM pctable;
Query OK, 4 rows affected (0.00 sec)
Records: 4  Duplicates: 0  Warnings: 0

mysql&gt; INSERT INTO pctable (parent_id) SELECT parent_id+4 FROM pctable;
Query OK, 8 rows affected (0.01 sec)
Records: 8  Duplicates: 0  Warnings: 0

mysql&gt; INSERT INTO pctable (parent_id) SELECT parent_id+5 FROM pctable;
Query OK, 16 rows affected (0.00 sec)
Records: 16  Duplicates: 0  Warnings: 0

mysql&gt; SELECT * FROM pctable;
+----+-----------+
| id | parent_id |
+----+-----------+
|  1 |         0 |
|  2 |         1 |
|  3 |         2 |
|  4 |         3 |
|  5 |         3 |
|  6 |         4 |
|  7 |         5 |
|  8 |         6 |
|  9 |         4 |
| 10 |         5 |
| 11 |         6 |
| 12 |         7 |
| 13 |         7 |
| 14 |         8 |
| 15 |         9 |
| 16 |        10 |
| 17 |         5 |
| 18 |         6 |
| 19 |         7 |
| 20 |         8 |
| 21 |         8 |
| 22 |         9 |
| 23 |        10 |
| 24 |        11 |
| 25 |         9 |
| 26 |        10 |
| 27 |        11 |
| 28 |        12 |
| 29 |        12 |
| 30 |        13 |
| 31 |        14 |
| 32 |        15 |
+----+-----------+
32 rows in set (0.00 sec)


Here are what the functions generate for each value:

mysql&gt; SELECT id,GetParentIDByID(id),GetAncestry(id) FROM pctable;
+----+---------------------+-----------------+
| id | GetParentIDByID(id) | GetAncestry(id) |
+----+---------------------+-----------------+
|  1 |                   0 |                 |
|  2 |                   1 | 1               |
|  3 |                   2 | 2,1             |
|  4 |                   3 | 3,2,1           |
|  5 |                   3 | 3,2,1           |
|  6 |                   4 | 4,3,2,1         |
|  7 |                   5 | 5,3,2,1         |
|  8 |                   6 | 6,4,3,2,1       |
|  9 |                   4 | 4,3,2,1         |
| 10 |                   5 | 5,3,2,1         |
| 11 |                   6 | 6,4,3,2,1       |
| 12 |                   7 | 7,5,3,2,1       |
| 13 |                   7 | 7,5,3,2,1       |
| 14 |                   8 | 8,6,4,3,2,1     |
| 15 |                   9 | 9,4,3,2,1       |
| 16 |                  10 | 10,5,3,2,1      |
| 17 |                   5 | 5,3,2,1         |
| 18 |                   6 | 6,4,3,2,1       |
| 19 |                   7 | 7,5,3,2,1       |
| 20 |                   8 | 8,6,4,3,2,1     |
| 21 |                   8 | 8,6,4,3,2,1     |
| 22 |                   9 | 9,4,3,2,1       |
| 23 |                  10 | 10,5,3,2,1      |
| 24 |                  11 | 11,6,4,3,2,1    |
| 25 |                   9 | 9,4,3,2,1       |
| 26 |                  10 | 10,5,3,2,1      |
| 27 |                  11 | 11,6,4,3,2,1    |
| 28 |                  12 | 12,7,5,3,2,1    |
| 29 |                  12 | 12,7,5,3,2,1    |
| 30 |                  13 | 13,7,5,3,2,1    |
| 31 |                  14 | 14,8,6,4,3,2,1  |
| 32 |                  15 | 15,9,4,3,2,1    |
+----+---------------------+-----------------+
32 rows in set (0.02 sec)


MORAL OF THE STORY : Recursive data retrieval must be scripted in MySQL

UPDATE 2011-10-24 17:17 EDT

Here is the reverse of GetAncestry. I call it GetFamilyTree.

Here is the algorithm:


Place Given ID in Queue
Loop

Dequeue into front_id
Retrieve all ids into queue_children whose parent_id = front_id
Append queue_children to retval_list (rv)
Enqueue queue_children 
Repeat until queue and queue_children are concurrently empty



I believe from my Data Structures and Algorithms classes in College, this is called something like preorder/prefix tree traversal.

Here is the code:

DELIMITER $$

DROP FUNCTION IF EXISTS `junk`.`GetFamilyTree` $$
CREATE FUNCTION `junk`.`GetFamilyTree` (GivenID INT) RETURNS varchar(1024) CHARSET latin1
DETERMINISTIC
BEGIN

    DECLARE rv,q,queue,queue_children VARCHAR(1024);
    DECLARE queue_length,front_id,pos INT;

    SET rv = '';
    SET queue = GivenID;
    SET queue_length = 1;

    WHILE queue_length &gt; 0 DO
        SET front_id = FORMAT(queue,0);
        IF queue_length = 1 THEN
            SET queue = '';
        ELSE
            SET pos = LOCATE(',',queue) + 1;
            SET q = SUBSTR(queue,pos);
            SET queue = q;
        END IF;
        SET queue_length = queue_length - 1;

        SELECT IFNULL(qc,'') INTO queue_children
        FROM (SELECT GROUP_CONCAT(id) qc
        FROM pctable WHERE parent_id = front_id) A;

        IF LENGTH(queue_children) = 0 THEN
            IF LENGTH(queue) = 0 THEN
                SET queue_length = 0;
            END IF;
        ELSE
            IF LENGTH(rv) = 0 THEN
                SET rv = queue_children;
            ELSE
                SET rv = CONCAT(rv,',',queue_children);
            END IF;
            IF LENGTH(queue) = 0 THEN
                SET queue = queue_children;
            ELSE
                SET queue = CONCAT(queue,',',queue_children);
            END IF;
            SET queue_length = LENGTH(queue) - LENGTH(REPLACE(queue,',','')) + 1;
        END IF;
    END WHILE;

    RETURN rv;

END $$


Here is what each row produces

mysql&gt; SELECT id,parent_id,GetParentIDByID(id),GetAncestry(id),GetFamilyTree(id) FROM pctable;
+----+-----------+---------------------+-----------------+--------------------------------------------------------------------------------------+
| id | parent_id | GetParentIDByID(id) | GetAncestry(id) | GetFamilyTree(id)                                                                    |
+----+-----------+---------------------+-----------------+--------------------------------------------------------------------------------------+
|  1 |         0 |                   0 |                 | 2,3,4,5,6,9,7,10,17,8,11,18,15,22,25,12,13,19,16,23,26,14,20,21,24,27,32,28,29,30,31 |
|  2 |         1 |                   1 | 1               | 3,4,5,6,9,7,10,17,8,11,18,15,22,25,12,13,19,16,23,26,14,20,21,24,27,32,28,29,30,31   |
|  3 |         2 |                   2 | 2,1             | 4,5,6,9,7,10,17,8,11,18,15,22,25,12,13,19,16,23,26,14,20,21,24,27,32,28,29,30,31     |
|  4 |         3 |                   3 | 3,2,1           | 6,9,8,11,18,15,22,25,14,20,21,24,27,32,31                                            |
|  5 |         3 |                   3 | 3,2,1           | 7,10,17,12,13,19,16,23,26,28,29,30                                                   |
|  6 |         4 |                   4 | 4,3,2,1         | 8,11,18,14,20,21,24,27,31                                                            |
|  7 |         5 |                   5 | 5,3,2,1         | 12,13,19,28,29,30                                                                    |
|  8 |         6 |                   6 | 6,4,3,2,1       | 14,20,21,31                                                                          |
|  9 |         4 |                   4 | 4,3,2,1         | 15,22,25,32                                                                          |
| 10 |         5 |                   5 | 5,3,2,1         | 16,23,26                                                                             |
| 11 |         6 |                   6 | 6,4,3,2,1       | 24,27                                                                                |
| 12 |         7 |                   7 | 7,5,3,2,1       | 28,29                                                                                |
| 13 |         7 |                   7 | 7,5,3,2,1       | 30                                                                                   |
| 14 |         8 |                   8 | 8,6,4,3,2,1     | 31                                                                                   |
| 15 |         9 |                   9 | 9,4,3,2,1       | 32                                                                                   |
| 16 |        10 |                  10 | 10,5,3,2,1      |                                                                                      |
| 17 |         5 |                   5 | 5,3,2,1         |                                                                                      |
| 18 |         6 |                   6 | 6,4,3,2,1       |                                                                                      |
| 19 |         7 |                   7 | 7,5,3,2,1       |                                                                                      |
| 20 |         8 |                   8 | 8,6,4,3,2,1     |                                                                                      |
| 21 |         8 |                   8 | 8,6,4,3,2,1     |                                                                                      |
| 22 |         9 |                   9 | 9,4,3,2,1       |                                                                                      |
| 23 |        10 |                  10 | 10,5,3,2,1      |                                                                                      |
| 24 |        11 |                  11 | 11,6,4,3,2,1    |                                                                                      |
| 25 |         9 |                   9 | 9,4,3,2,1       |                                                                                      |
| 26 |        10 |                  10 | 10,5,3,2,1      |                                                                                      |
| 27 |        11 |                  11 | 11,6,4,3,2,1    |                                                                                      |
| 28 |        12 |                  12 | 12,7,5,3,2,1    |                                                                                      |
| 29 |        12 |                  12 | 12,7,5,3,2,1    |                                                                                      |
| 30 |        13 |                  13 | 13,7,5,3,2,1    |                                                                                      |
| 31 |        14 |                  14 | 14,8,6,4,3,2,1  |                                                                                      |
| 32 |        15 |                  15 | 15,9,4,3,2,1    |                                                                                      |
+----+-----------+---------------------+-----------------+--------------------------------------------------------------------------------------+
32 rows in set (0.04 sec)


This algorithm works cleanly provided there are no cyclic paths. If there exists any cyclic paths, you would have to add a 'visited' column to the table.

Once you add visited column, here is the algorithm blocking cyclic relationships:


Place Given ID in Queue
Mark all visited with 0
Loop

Dequeue into front_id
Retrieve all ids into queue_children whose parent_id = front_id and visited = 0
Mark all queue_children just retrieved with visited = 1
Append queue_children to retval_list (rv)
Enqueue queue_children 
Repeat until queue and queue_children are concurrently empty



UPDATE 2011-10-24 17:37 EDT

I created a new table called observations and populated your sample data. I changed the stored procedures to use observations instead of pctable. Here is your output:

mysql&gt; CREATE TABLE observations LIKE pctable;
Query OK, 0 rows affected (0.04 sec)

mysql&gt; INSERT INTO observations VALUES (1,3), (2,5), (3,0), (4,10),(5,0),(6,1),(7,5),(8,10),(9,10),(10,3);
Query OK, 10 rows affected (0.00 sec)
Records: 10  Duplicates: 0  Warnings: 0

mysql&gt; SELECT * FROM observations;
+----+-----------+
| id | parent_id |
+----+-----------+
|  1 |         3 |
|  2 |         5 |
|  3 |         0 |
|  4 |        10 |
|  5 |         0 |
|  6 |         1 |
|  7 |         5 |
|  8 |        10 |
|  9 |        10 |
| 10 |         3 |
+----+-----------+
10 rows in set (0.00 sec)

mysql&gt; SELECT id,parent_id,GetParentIDByID(id),GetAncestry(id),GetFamilyTree(id) FROM observations;
+----+-----------+---------------------+-----------------+-------------------+
| id | parent_id | GetParentIDByID(id) | GetAncestry(id) | GetFamilyTree(id) |
+----+-----------+---------------------+-----------------+-------------------+
|  1 |         3 |                   3 |                 | 6                 |
|  2 |         5 |                   5 | 5               |                   |
|  3 |         0 |                   0 |                 | 1,10,6,4,8,9      |
|  4 |        10 |                  10 | 10,3            |                   |
|  5 |         0 |                   0 |                 | 2,7               |
|  6 |         1 |                   1 | 1               |                   |
|  7 |         5 |                   5 | 5               |                   |
|  8 |        10 |                  10 | 10,3            |                   |
|  9 |        10 |                  10 | 10,3            |                   |
| 10 |         3 |                   3 | 3               | 4,8,9             |
+----+-----------+---------------------+-----------------+-------------------+
10 rows in set (0.01 sec)


UPDATE 2011-10-24 18:22 EDT

I changed the code for GetAncestry. There was WHILE ch &gt; 1 it should be WHILE ch &gt; 0

mysql&gt; SELECT id,parent_id,GetParentIDByID(id),GetAncestry(id),GetFamilyTree(id) FROM observations;
+----+-----------+---------------------+-----------------+-------------------+
| id | parent_id | GetParentIDByID(id) | GetAncestry(id) | GetFamilyTree(id) |
+----+-----------+---------------------+-----------------+-------------------+
|  1 |         3 |                   3 | 3               | 6                 |
|  2 |         5 |                   5 | 5               |                   |
|  3 |         0 |                   0 |                 | 1,10,6,4,8,9      |
|  4 |        10 |                  10 | 10,3            |                   |
|  5 |         0 |                   0 |                 | 2,7               |
|  6 |         1 |                   1 | 1,3             |                   |
|  7 |         5 |                   5 | 5               |                   |
|  8 |        10 |                  10 | 10,3            |                   |
|  9 |        10 |                  10 | 10,3            |                   |
| 10 |         3 |                   3 | 3               | 4,8,9             |
+----+-----------+---------------------+-----------------+-------------------+
10 rows in set (0.01 sec)


Try it now !!!