SELECT * FROM `mytable` ORDER BY `display_order` DESC;

UPDATE `my_dispaly_order_table` SET `display_order`='1,9,2,6,23';

UPDATE `mytable` SET `display_order`='1' WHERE `rowId` = 1;
UPDATE `mytable` SET `display_order`='2' WHERE `rowId` = 9;
UPDATE `mytable` SET `display_order`='3' WHERE `rowId` = 2;
UPDATE `mytable` SET `display_order`='4' WHERE `rowId` = 6;
UPDATE `mytable` SET `display_order`='5' WHERE `rowId` = 23;

-- Move #10 down (i.e. swap #10 and #11)
UPDATE mytable SET display_order =
  CASE display_order
    WHEN 10 THEN 11
    WHEN 11 THEN 10
  END CASE
WHERE display_order BETWEEN 10 AND 11;

-- Move #4 to #10
UPDATE mytable SET display_order
  CASE display_order
    WHEN 4 THEN 10
    ELSE display_order - 1
  END CASE
WHERE display_order BETWEEN 4 AND 10;

-- Swap in two steps will not work as demostrated here:

UPDATE mytable SET display_order = 10 WHERE display_order = 11;
-- Now you have two entries with display_order = 10

UPDATE mytable SET display_order = 11 WHERE display_order = 10;
-- Now you have two entries with display_order = 11 (both have been changed)

UPDATE mytable SET display_order =
  CASE id
    WHEN 10 THEN 1
    WHEN 23 THEN 2
    WHEN 4 THEN 3
  END CASE
WHERE id IN (10, 23, 4)

$new_order = array(4, 2, 99, 15, 32); // etc

$query = "UPDATE mytable SET display_order = (CASE id ";
foreach($new_order as $sort => $id) {
  $query .= " WHEN {$id} THEN {$sort}";
}
$query .= " END) WHERE id IN (" . implode(",", $new_order) . ")";

UPDATE table SET col=col+1 WHERE col > 10
UPDATE table SET col=10 WHERE id = X
...

Order    Item
-----    ----
1        Original Item 1
2        Original Item 2
3        Original Item 3
4        Original Item 4
5        Original Item 5

Order    Item
-----    ----
1        Original Item 1
1.5      Original Item 4
2        Original Item 2
3        Original Item 3
5        Original Item 5

Order    Item
-----    ----
1        Original Item 1
1.5      Original Item 4
1.75     Original Item 3
2        Original Item 2
5        Original Item 5

CREATE TABLE t_list (
        id INT NOT NULL PRIMARY KEY,
        parent INT NOT NULL,
        value VARCHAR(50) NOT NULL,
        /* Don't forget to create an index on PARENT */
        KEY ix_list_parent ON (parent)
)

id   parent  value

1    0       Value1
2    3       Value2
3    4       Value3
4    1       Value4

SELECT  @r := (
        SELECT  id
        FROM    t_list
        WHERE   parent = @r
        ) AS id
FROM    (
        SELECT  @r := 0
        ) vars,
        t_list

id   parent  value

1    0       Value1
4    1       Value4
3    4       Value3
2    3       Value2

UPDATE table SET display_order = display_order -1 WHERE display_order BETWEEN 10 AND 12
UPDATE table SET display_order = 12 WHERE row_id = [id of what was row 10]

function reOrderRows($tablename, $ordercol, $idsarray){

    $query = "UPDATE $tablename SET $ordercol = (CASE $ordercol ";
    foreach($idsarray as $prev => $new) {
      $query .= " WHEN $prev THEN $newn";
    }
    $query .= " END) WHERE $ordercol IN (" . implode(",", array_keys($idsarray)) . ")";

    mysql_query($query);
}

function swapRows($tablename, $ordercol, $firstid, $secondid){
    $swaparray = array("$firstid" => "$secondid", "$secondid" => "$firstid");
    reOrderRows($tablename, $ordercol, $swaparray);
}