Simple solution:
UPDATE table
SET words = REPLACE(words, 'brown', 'green')
WHERE words REGEXP 'brown ' OR words REGEXP ' brown'
Better solution from http://techras.wordpress.com/2011/06/02/regex-replace-for-mysql/:
SET sql_mode='NO_BACKSLASH_ESCAPES';
DELIMITER $$
CREATE FUNCTION `regex_replace`(pattern VARCHAR(1000),replacement VARCHAR(1000),original VARCHAR(1000))
RETURNS VARCHAR(1000)
DETERMINISTIC
BEGIN
DECLARE temp VARCHAR(1000);
DECLARE ch VARCHAR(1);
DECLARE i INT;
SET i = 1;
SET temp = '';
IF original REGEXP pattern THEN
loop_label: LOOP
IF i>CHAR_LENGTH(original) THEN
LEAVE loop_label;
END IF;
SET ch = SUBSTRING(original,i,1);
IF NOT ch REGEXP pattern THEN
SET temp = CONCAT(temp,ch);
ELSE
SET temp = CONCAT(temp,replacement);
END IF;
SET i=i+1;
END LOOP;
ELSE
SET temp = original;
END IF;
RETURN temp;
END$$
DELIMITER ;