MySQL Select Date Equal to Today

SELECT users.id, DATE_FORMAT(users.signup_date, '%Y-%m-%d') 
FROM users 
WHERE DATE(signup_date) = CURDATE()

This query will use index if you have it for signup_date field

SELECT users.id, DATE_FORMAT(users.signup_date, '%Y-%m-%d') 
    FROM users 
    WHERE signup_date >= CURDATE() && signup_date < (CURDATE() + INTERVAL 1 DAY)

Sounds like you need to add the formatting to the WHERE:

SELECT users.id, DATE_FORMAT(users.signup_date, '%Y-%m-%d') 
FROM users 
WHERE DATE_FORMAT(users.signup_date, '%Y-%m-%d') = CURDATE()

See SQL Fiddle with Demo