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;

I think you're after something like this

select c.[customer ID], [some date], balance
from [cust date table] c
inner join 
    ( select [customer ID], MAX([some date]) as maxdate
    from [cust date table]
    group by [customer ID]) c2
on c2.[customer ID] = c.[customer ID]
and c2.maxdate = c.[some date]

There are a number of variations on this, i.e. CTE, table variable, #table, that you can play around with to see what gives you the best performance in your situation.