Starting with MySQL 4.1, all subquery forms and operations that the SQL standard requires are supported, as well as a few features that are MySQL-specific.

The queries:
 
SELECT * FROM t1 WHERE id NOT IN (SELECT id FROM t2);
SELECT * FROM t1 WHERE NOT EXISTS (SELECT id FROM t2 WHERE t1.id=t2.id);
 
Can be rewritten as:
 
SELECT table1.* FROM table1 LEFT JOIN table2 ON table1.id=table2.id
                                       WHERE table2.id IS NULL;

What kind of store is present in no cities?
 
SELECT DISTINCT store_type FROM Stores
  WHERE NOT EXISTS (SELECT * FROM Cities_Stores
                    WHERE Cities_Stores.store_type = Stores.store_type);