There is a more effective way of generating an intersect, by using UNION ALL and GROUP BY. Performances are twice better according to my tests on large datasets.
Example:
SELECT t1.value from (
(SELECT DISTINCT value FROM table_a)
UNION ALL
(SELECT DISTINCT value FROM table_b)
) AS t1 GROUP BY value HAVING count(*) >= 2;
It is more effective, because with the INNER JOIN solution, MySQL will look up for the results of the first query, then for each row, look up for the result in the second query. With the UNION ALL-GROUP BY solution, it will query results of the first query, results of the second query, then group the results all together at once.