SELECT CustomerID, OrderDate
FROM Orders
ORDER BY CustomerID;

SELECT CustomerId, OrderDate
FROM Orders as ExtOrders
WHERE OrderId IN (
     SELECT TOP 4 OrderId
     FROM Orders
     WHERE CustomerId LIKE ExtOrders.CustomerId
     ORDER BY OrderDate DESC)
ORDER BY CustomerId; -- Might not work in SQLFiddle if CustomerId is text

SELECT CustomerId, OrderDate
FROM Orders as ExtOrders
WHERE OrderId IN (
     SELECT TOP 4 OrderId
     FROM Orders
     WHERE CustomerId LIKE ExtOrders.CustomerId
     ORDER BY OrderDate DESC)
ORDER BY CustomerId; -- Might not work in SQLFiddle if CustomerId is text

SELECT CustomerID, OrderDate
FROM (SELECT o.*,
             ROW_NUMBER() OVER (PARTITION BY CustomerId ORDER BY OrderDate DESC) as seqnum
      FROM Orders
     ) o
WHERE seqnum <= 4
ORDER BY CustomerID;

Use Northwind_2012
WITH e
AS (
    SELECT ROW_NUMBER() OVER (
            PARTITION BY CustomerID ORDER BY OrderDate DESC
            ) AS rownum
        ,CustomerID
        ,OrderDate
    FROM Orders
    )
SELECT CustomerID
    ,OrderDate
FROM e
WHERE rownum <= 4