How do I change all empty strings to NULL in a table?

For newbies, you may still need more work after seeing the above answers. And it's not realistic to type thousands lines. So here I provide a complete working code to let you avoid syntax errors etc.

DROP PROCEDURE IF EXISTS processallcolumns;

DELIMITER $$

CREATE PROCEDURE processallcolumns ()
BEGIN

  DECLARE i,num_rows INT ;
  DECLARE col_name char(250);

  DECLARE col_names CURSOR FOR
  SELECT column_name
  FROM INFORMATION_SCHEMA.COLUMNS
  WHERE table_name = 'PROCESSINGTABLE'
  ORDER BY ordinal_position;

  OPEN col_names ;
  select FOUND_ROWS() into num_rows;

  SET i = 1;
  the_loop: LOOP

     IF i > num_rows THEN
          CLOSE col_names;
          LEAVE the_loop;
      END IF;


      FETCH col_names 
      INTO col_name;     


      SET @command_text = CONCAT('UPDATE `PROCESSINGTABLE` SET ', col_name, '= IF(LENGTH(', col_name, ')=0, NULL,', col_name, ') WHERE 1 ;' ) ;

--      UPDATE `PROCESSINGTABLE` SET col_name=IF(LENGTH(col_name)=0,NULL,col_name) WHERE 1;
--      This won't work, because MySQL doesn't take varibles as column name.

      PREPARE stmt FROM @command_text ;
      EXECUTE stmt ;

      SET i = i + 1;  
  END LOOP the_loop ;



END$$
DELIMITER ;

call processallcolumns ();
DROP PROCEDURE processallcolumns;

UPDATE
    TableName
SET
    column01 = CASE column01 WHEN '' THEN NULL ELSE column01 END,
    column02 = CASE column02 WHEN '' THEN NULL ELSE column02 END,
    column03 = CASE column03 WHEN '' THEN NULL ELSE column03 END,
    ...,
    column99 = CASE column99 WHEN '' THEN NULL ELSE column99 END

This is still doing it manually, but is slightly less painful than what you have because it doesn't require you to send a query for each and every column. Unless you want to go to the trouble of scripting it, you will have to put up with a certain amount of pain when doing something like this.

Edit: Added the ENDs

One possible script:

for col in $(echo "select column_name from information_schema.columns
where table_name='$TABLE'"|mysql --skip-column-names $DB)
do
echo update $TABLE set $col = NULL where $col = \'\'\;
done|mysql $DB