I took Saggi's answer and thought about modifying it so that it would show birthdays for next 7 days and noticed it also neatly solves the leap year problem :)
SELECT *
FROM USERS
WHERE
DATE_FORMAT(FROM_UNIXTIME(birthDate),'%m-%d') >= DATE_FORMAT(NOW(),'%m-%d') AND
DATE_FORMAT(FROM_UNIXTIME(birthDate),'%m-%d') < DATE_FORMAT(NOW()+INTERVAL 1 DAY,'%m-%d')
Note it doesn't include the upper bound. For leap years nothing falls between '02-28' and '02-29', but for non-leap years the '02-29' falls between '02-28' and '03-01'.
If you'd want the next 7 days, use:
SELECT *
FROM USERS
WHERE
DATE_FORMAT(FROM_UNIXTIME(birthDate),'%m-%d') BETWEEN
DATE_FORMAT(NOW(),'%m-%d') AND DATE_FORMAT(NOW()+INTERVAL 7 DAY,'%m-%d')