Update: Changed 0×00 to '\0' as per Jan-Hendrik's comment below.

There are a number of MySQL functions for calculating Levenshtein distance floating around StackOverflow and other forums. They all seem to be based off http://codejanitor.com/wp/2007/02/10/levenshtein-distance-as-a-mysql-stored-function/ (broken link).

Anyway, I couldn't get them to work for me. MySQL complained:

ERROR 1064 (42000): You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near '' at line 4
 

Well, it turns out that you need to specify a delimiter instead of the default delimiter of ;. So here's a working version of the levenstein distance function, courtesy of CodeJanitor.

DELIMITER //
CREATE FUNCTION LEVENSHTEIN (s1 VARCHAR(255), s2 VARCHAR(255))
RETURNS INT
DETERMINISTIC
BEGIN
  DECLARE s1_len, s2_len, i, j, c, c_temp, cost INT;
  DECLARE s1_char CHAR;
  DECLARE cv0, cv1 VARBINARY(256);
  SET s1_len = CHAR_LENGTH(s1), s2_len = CHAR_LENGTH(s2), cv1 = '\0', j = 1, i = 1, c = 0;
  IF s1 = s2 THEN
    RETURN 0;
  ELSEIF s1_len = 0 THEN
    RETURN s2_len;
  ELSEIF s2_len = 0 THEN
    RETURN s1_len;
  ELSE
    WHILE j <= s2_len DO
      SET cv1 = CONCAT(cv1, UNHEX(HEX(j))), j = j + 1;
    END WHILE;
    WHILE i <= s1_len DO
      SET s1_char = SUBSTRING(s1, i, 1), c = i, cv0 = UNHEX(HEX(i)), j = 1;
      WHILE j <= s2_len DO
        SET c = c + 1;
        IF s1_char = SUBSTRING(s2, j, 1) THEN SET cost = 0; ELSE SET cost = 1; END IF;
        SET c_temp = CONV(HEX(SUBSTRING(cv1, j, 1)), 16, 10) + cost;
        IF c > c_temp THEN SET c = c_temp; END IF;
        SET c_temp = CONV(HEX(SUBSTRING(cv1, j+1, 1)), 16, 10) + 1;
        IF c > c_temp THEN SET c = c_temp; END IF;
        SET cv0 = CONCAT(cv0, UNHEX(HEX(c))), j = j + 1;
      END WHILE;
      SET cv1 = cv0, i = i + 1;
    END WHILE;
  END IF;
  RETURN c;
END//