Returning a result set with multiple rows based on max date
You simply want:

SELECT
    [Customer ID],
    MAX([Some Date]) AS[Latest Date]
FROM[Cust Date TABLE]
GROUP BY
    [Customer ID];


Ok - you've revised it. You now want to order the rows and pick the top one:

WITH numbered AS (
    SELECT
        [Customer ID],
        [Some Date],
        [Balance],
        ROW_NUMBER() OVER (
            PARTITION BY
                [Customer ID]
            ORDER BY
                [Some Date] DESC
        ) AS rownum
    FROM[Cust Date TABLE]
)
SELECT
    [Customer ID],
    [Some Date],
    [Balance]
FROM numbered
WHERE
    rownum = 1;