MS SQL Server - update row value to next row with row id
It can be done in one set based operation
Using a WHILE risks invoking the "Halloween problem" as you update rows over and over.

It's easier with SQL Server 2012 using LAG

DECLARE @t TABLE
(
    Newid1 int
    , a int  NULL
    , b int
    , c int
);

INSERT INTO @t VALUES(1, NULL, 40, 50)
        ,(2, NULL, 45, 55) ,(3, NULL, 46, 56)
        ,(4, NULL, 47, 57) ,(5, NULL, 48, 58);

-- SQL Server 2012
WITH t AS
(
    SELECT a, LAG(c) OVER (ORDER BY Newid1) AS nextC
    FROM @t
)
UPDATE t SET a = nextC;

SELECT * FROm @t;


But for SQL Server 2005+

DECLARE @t TABLE
(
    Newid1 int
    , a int  NULL
    , b int
    , c int
);

-- SQL Server 2005+
WITH t AS
(
    SELECT Newid1, ROW_NUMBER() OVER (ORDER BY Newid1) +1 AS nextID, a, c
    FROM @t
)
UPDATE t1
SET a = t2.c
FROM
   t AS t1
   JOIN
   t AS t2 ON t1.Newid1 = t2.nextID;

SELECT * FROM @t;