MySQL INNER JOIN select only one row from second table

SELECT u.*, p.*
FROM users AS u
INNER JOIN payments AS p ON p.id = (
    SELECT id
    FROM payments AS p2
    WHERE p2.user_id = u.id
    ORDER BY date DESC
    LIMIT 1
)

Or

SELECT u.*, p.*
FROM users AS u
INNER JOIN payments AS p ON p.user_id = u.id
WHERE NOT EXISTS (
    SELECT 1
    FROM payments AS p2
    WHERE
        p2.user_id = p.user_id AND
        (p2.date > p.date OR (p2.date = p.date AND p2.id > p.id))
)

These solutions are better than the accepted answer because they work correctly when there are multiple payments with same user and date. You can try on SQL Fiddle.

You need to have a subquery to get their latest date per user ID.

SELECT  a.*, c.*
FROM users a 
    INNER JOIN payments c
        ON a.id = c.user_ID
    INNER JOIN
    (
        SELECT user_ID, MAX(date) maxDate
        FROM payments
        GROUP BY user_ID
    ) b ON c.user_ID = b.user_ID AND
            c.date = b.maxDate
WHERE a.package = 1