próximos aniversários do mySQL SELECT

Para obter todos os aniversários nos próximos 7 dias, adicione a diferença de ano entre a data de nascimento e hoje à data de nascimento e descubra se ela cai nos próximos sete dias.

SELECT * 
FROM  persons 
WHERE  DATE_ADD(birthday, 
                INTERVAL YEAR(CURDATE())-YEAR(birthday)
                         + IF(DAYOFYEAR(CURDATE()) > DAYOFYEAR(birthday),1,0)
                YEAR)  
            BETWEEN CURDATE() AND DATE_ADD(CURDATE(), INTERVAL 7 DAY);

Se você quiser excluir os aniversários de hoje, basta alterar > para >=

SELECT * 
FROM  persons 
WHERE  DATE_ADD(birthday, 
                INTERVAL YEAR(CURDATE())-YEAR(birthday)
                         + IF(DAYOFYEAR(CURDATE()) >= DAYOFYEAR(birthday),1,0)
                YEAR)  
            BETWEEN CURDATE() AND DATE_ADD(CURDATE(), INTERVAL 7 DAY);

-- Same as above query with another way to exclude today's birthdays 
SELECT * 
FROM  persons 
WHERE  DATE_ADD(birthday, 
                INTERVAL YEAR(CURDATE())-YEAR(birthday)
                         + IF(DAYOFYEAR(CURDATE()) > DAYOFYEAR(birthday),1,0)
                YEAR) 
            BETWEEN CURDATE() AND DATE_ADD(CURDATE(), INTERVAL 7 DAY)
     AND DATE_ADD(birthday, INTERVAL YEAR(CURDATE())-YEAR(birthday) YEAR) <> CURDATE();


-- Same as above query with another way to exclude today's birthdays 
SELECT * 
FROM  persons 
WHERE  DATE_ADD(birthday, 
                INTERVAL YEAR(CURDATE())-YEAR(birthday)
                         + IF(DAYOFYEAR(CURDATE()) > DAYOFYEAR(birthday),1,0)
                YEAR) 
            BETWEEN CURDATE() AND DATE_ADD(CURDATE(), INTERVAL 7 DAY)
     AND (MONTH(birthday) <> MONTH(CURDATE()) OR DAY(birthday) <> DAY(CURDATE()));

Aqui está uma DEMO de todas as consultas