How to change identity column values programmatically?

IDENTITY column values are immutable.

However it is possible to switch the table metadata to remove the IDENTITY property, do the update, then switch back.

Assuming the following structure

CREATE TABLE Test
(
ID INT IDENTITY(1,1) PRIMARY KEY,
X VARCHAR(10)
)

INSERT INTO Test 
OUTPUT INSERTED.*
SELECT 'Foo' UNION ALL
SELECT 'Bar' UNION ALL
SELECT 'Baz'

Then you can do

/*Define table with same structure but no IDENTITY*/
CREATE TABLE Temp
(
ID INT PRIMARY KEY,
X VARCHAR(10)
)

/*Switch table metadata to new structure*/
ALTER TABLE Test SWITCH TO Temp;

/*Do the update*/
UPDATE Temp SET ID = ID + 1;

/*Switch table metadata back*/
ALTER TABLE Temp SWITCH TO Test;

/*ID values have been updated*/
SELECT *
FROM Test

/*Safety check in case error in preceding step*/
IF NOT EXISTS(SELECT * FROM Temp)
    DROP TABLE Temp /*Drop obsolete table*/

In SQL Server 2012 it is possible to have an auto incrementing column that can also be updated more straightforwardly with SEQUENCES

CREATE SEQUENCE Seq
    AS INT
    START WITH 1
    INCREMENT BY 1

CREATE TABLE Test2
(
ID INT DEFAULT NEXT VALUE FOR Seq NOT NULL PRIMARY KEY,
X VARCHAR(10)
)

INSERT INTO Test2(X)
SELECT 'Foo' UNION ALL
SELECT 'Bar' UNION ALL
SELECT 'Baz'

UPDATE Test2 SET ID+=1

You need to

set identity_insert YourTable ON

Then delete your row and reinsert it with different identity.

Once you have done the insert don't forget to turn identity_insert off

set identity_insert YourTable OFF