I've found an answer to this problem :)
SET @update_id := 0;
UPDATE some_table SET column_name = 'value', id = (SELECT @update_id := id)
WHERE some_other_column = 'blah' LIMIT 1;
SELECT @update_id;
EDIT by aefxx
This technique can be further expanded to retrieve the ID of every row affected by an update statement:
SET @uids := null;
UPDATE footable
SET foo = 'bar'
WHERE fooid > 5
AND ( SELECT @uids := CONCAT_WS(',', fooid, @uids) );
SELECT @uids;
This will return a string with all the IDs concatenated by a comma.
If you are only doing insertions, and want one from the same session, do as per peirix's answer. If you are doing modifications, you will need to modify your database schema to store which entry was most recently updated.
If you want the id from the last modification, which may have been from a different session (i.e. not the one that was just done by the PHP code running at present, but one done in response to a different request), you can add a TIMESTAMP column to your table called last_modified (see http://dev.mysql.com/doc/refman/5.1/en/datetime.html for information), and then when you update, set last_modified=CURRENT_TIME.
Having set this, you can then use a query like: SELECT id FROM table ORDER BY last_modified DESC LIMIT 1; to get the most recently modified row.
No need for so long Mysql code. In PHP, query should look something like this:
$updateQuery = mysql_query("UPDATE table_name SET row='value' WHERE id='$id'") or die ('Error');
$lastUpdatedId = mysql_insert_id();