En MySQL no existe este tipo de JOIN, pero se puede emular mediante UNION:

Con dos tablas:

SELECT * FROM t1
LEFT JOIN t2 ON t1.id = t2.id
UNION
SELECT * FROM t1
RIGHT JOIN t2 ON t1.id = t2.id

Con 3 tablas

SELECT * FROM t1
LEFT JOIN t2 ON t1.id = t2.id
LEFT JOIN t3 ON t2.id = t3.id
UNION
SELECT * FROM t1
RIGHT JOIN t2 ON t1.id = t2.id
LEFT JOIN t3 ON t2.id = t3.id
UNION
SELECT * FROM t1
RIGHT JOIN t2 ON t1.id = t2.id
RIGHT JOIN t3 ON t2.id = t3.id

• Why does MySQL report a syntax error on FULL OUTER JOIN? (Stack Overflow)

Seleccionar los registros de una tabla que no aparezcan en la otra:

SELECT *
FROM table1 t1
LEFT JOIN table2 t2 ON t2.id = t1.id
WHERE t2.id IS NULL